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Waves and
Vibrations: Waves
Waves
Other Waves
Mathematics and Waves
Wave Speed
Energy in Waves
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Waves and
Vibrations: Waves
(continued)
Wave Behavior and Interaction
Standing Waves on a String
Waves on Strings
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Waves and Vibrations: Waves > Waves
Waves
• Waves
• Transverse Waves
• Longitudinal Waves
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Waves and Vibrations: Waves > Waves
Waves
• A wave can be thought of as a disturbance or oscillation that travels through
space-time, accompanied by a transfer of energy.
• The direction a wave propagates is perpendicular to the direction it oscillates for
transverse waves.
• A wave does not move mass in the direction of propagation; it transfers energy.
Wave motion
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Waves and Vibrations: Waves > Waves
Transverse Waves
• Transverse waves oscillate in the z-y plane but travel along the x axis.
• A transverse wave has a speed of propagation given by the equation v = fλ.
• The direction of energy transfer is perpendicular to the motion of the wave.
Sine Wave
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Waves and Vibrations: Waves > Waves
Longitudinal Waves
• While longitudinal waves oscillate in the direction of propagation, they do not
displace mass since the oscillations are small and involve an equilibrium position.
• The longitudinal 'waves' can be conceptualized as pulses that transfer energy
along the axis of propagation.
• Longitudinal waves can be conceptualized as pressure waves characterized by
compression and rarefaction.
Longitudinal Waves
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Waves and Vibrations: Waves > Other Waves
Other Waves
• Water Waves
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Waves and Vibrations: Waves > Other Waves
Water Waves
• The particles which make up a water wave move in circular paths.
• If the waves move slower than the wind above them, energy is transfered from
the wind to the waves.
• The oscillations are greatest on the surface of the wave and become weaker
deeper in the fluid.
Water waves
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Waves and Vibrations: Waves > Mathematics and Waves
Mathematics and Waves
• Mathematical Represenation of a Traveling Wave
• Energy, Intensity, Frequency, and Amplitude
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Waves and Vibrations: Waves > Mathematics and Waves
Mathematical Represenation of a Traveling Wave
• Any function u(x,t) satisfying [Equation 1] is a solution the wave equation. To solve this new
equation, we introduced new variables [Equation 2].
Equation 1
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Wave Equation in Two Dimensions
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Equation 2
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Waves and Vibrations: Waves > Mathematics and Waves
Mathematical Represenation of a Traveling Wave
• The solutions of the 1D wave equation are sums of a left traveling function and a
right traveling function.
• The wave function is further determined by taking additional information, usually
given as boundary conditions and some others.
Wave Equation in Two Dimensions
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Waves and Vibrations: Waves > Mathematics and Waves
Energy, Intensity, Frequency, and Amplitude
• The energy effects of a wave depend on the amplitude and duration (time) of the
wave. Waves can also be concentrated or spread out. Considering all these
factors, intensity is defined as power per unit area.
• In the classical wave theory, energy of a wave doesn't depend on the frequency
of the wave. However, the energy of individual photons in a beam is determined
by the frequency of the beam.
• Wave's energy is directly proportional to its amplitude squared.
Earthquake Destruction
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Waves and Vibrations: Waves > Wave Speed
Wave Speed
• Wavelength, Freqency in Relation to Speed
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Waves and Vibrations: Waves > Wave Speed
Wavelength, Freqency in Relation to Speed
• The wavelength is the spatial period of the wave.
• The frequency of a wave refers to the number of cycles per unit time and is not to
be confused with angular frequency.
• The phase velocity can be expressed as the product of wavelength and
frequency.
Frequencies of different sine waves.
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Waves and Vibrations: Waves > Energy in Waves
Energy in Waves
• Energy Transportation
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Waves and Vibrations: Waves > Energy in Waves
Energy Transportation
• Waves which are more massive transfer more energy.
• Waves with greater velocities transfer more energy.
• Energy of a wave is transported in the direction of the waves transportation.
Water Wave
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Wave Behavior and Interaction
• Superposition and Interference
• Reflection and Transmission
• Standing Waves and Resonance
• Harmonic Wave Functions
• Refraction
• Diffraction
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Superposition and Interference
• The disturbances of waves are superimposed when they come together—a
phenomenon called superposition.
• As a result of superposition of waves, inteference can be observed. Interference
is an effect caused by two or more waves. Waves can interfere constructively or
destructively.
• The superposition of most waves produces a combination of constructive and
destructive interference and can vary from place to place and time to time.
Complex Pattern of Waves
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Reflection and Transmission
• Reflection is a wave phenomenon that changes the direction of a wavefront at an
interface between two different media so that the wavefront returns into the
medium from which it originated.
• At the boundary, a wave must be continuous and there should be no kinks in it.
• By imposing boundary conditions, we can solve wave equation and get the form
of the waves. Reflection and transmission coefficients are defined as ratio of
reflected/transmitted amplitudes and the incoming amplitude.
Partial Transmittance and Partial Reflectance
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Standing Waves and Resonance
• If two waves with the same amplitude and wavelength travel in opposite directions
they alternate between constructive and destructive interference. The resultant
looks like a wave standing in place and, thus, is called a standing wave.
• Nodes are points of no motion in standing waves. An antinode is the location of
maximum amplitude of a standing wave.
• During an earthquake, buildings with a certain height may collapse more easily.
This occurs when the building height matches the condition for setting up a
standing wave for that particular height.
Standing Wave
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Harmonic Wave Functions
• We represent harmonic wave motion in terms of either harmonic sine or cosine function: [Equation
3].
Equation 3
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Harmonic Waves
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Harmonic Wave Functions
• k and ω in the harmonic wave functinon are related to wavelength and period as follows: [Equation
4].
Equation 4
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Harmonic Waves
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Harmonic Wave Functions
• The speed of a harmonic wave is given by ω/k.
Harmonic Waves
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Refraction
• Refraction is mainly in governance to the law of conservation of energy and
momentum. Due to change of medium, the phase velocity of the wave is changed
but its frequency remains constant.
Refraction in Water
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Waves and Vibrations: Waves > Wave Behavior and Interaction
• Refraction is described by Snell's law, which states that for a given pair of media and a wave with a
single frequency, [Equation 5].
Equation 5
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Waves and Vibrations: Waves > Wave Behavior and Interaction
• An object partially immersed in water looks bent due to refraction.
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Waves and Vibrations: Waves > Wave Behavior and Interaction
Diffraction
• Diffraction is a wave phenomenon. It occurs with all waves, including sound
waves, water waves, and electromagnetic waves such as visible light, X-rays and
radio waves.
• Diffraction effects are generally most pronounced for waves whose wavelengths
are roughly similar to the dimensions of the diffracting objects.
• The effects of diffraction are often seen in everyday life. All these effects are a
consequence of the fact that light propagates as a wave.
Intensity Pattern
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Waves and Vibrations: Waves > Standing Waves on a String
Standing Waves on a String
• Standing Waves on a String
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Waves and Vibrations: Waves > Standing Waves on a String
Standing Waves on a String
• The reflected wave is inverted from the incident wave when a transverse wave on
a string is fixed at the end point. The reflected wave is not inverted from the
incident wave when a transverse wave on a string is free at the end point.
• A standing wave occurs when an incident wave meets a reflected wave on a
string.
• A standing wave contains nodes (points that remain flat due to the destructive
interference) and antinodes (points with maximum oscillation due to the
constructive interference).
• Every point in the string oscillates up and down and the amplitude of the
oscillations depends on the location of the point.
Free End Reflection
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• A standing wave has some points that remain flat due to destructive interference.
These are called antinodes.
• The points on a standing wave that have reached maximum oscillation do so from
constructive interference, and are called nodes.
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Waves and Vibrations: Waves > Waves on Strings
Waves on Strings
• The Speed of a Wave on a String
• Reflections
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Waves and Vibrations: Waves > Waves on Strings
The Speed of a Wave on a String
• The type of wave that occurs in a string is called a transverse wave. In a
transverse wave, the wave direction is perpendicular the the direction that the
string oscillates in.
Figure 1
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Waves and Vibrations: Waves > Waves on Strings
• The period of a wave is indirectly proportional to the frequency of the wave: [Equation 6].
Equation 6
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Waves and Vibrations: Waves > Waves on Strings
• The speed of a wave is proportional to the wavelength and indirectly proportional to the period of the
wave: [Equation 7].
Equation 7
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Waves and Vibrations: Waves > Waves on Strings
• This equation can be simplified by using the relationship between frequency and period: [Equation
8].
Equation 8
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Waves and Vibrations: Waves > Waves on Strings
Reflections
• When a transverse wave on a string is fixed at the end point, the reflected wave is
inverted from the incident wave. When a transverse wave on a string is free at the
end point, the reflected wave is not inverted from the incident wave.
• A standing wave occurs when an incident wave meets a reflected wave on a
string.
• The points in a standing wave that appear to remain flat and do not move are
called nodes. The points which reach the maximum oscillation height are called
antinodes.
• Every point in the medium containing a standing wave oscillates up and down and
the amplitude of the oscillations depends on the location of the point.
Transverse Wave
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• A standing wave has some points that remain flat due to destructive interference.
These are called antinodes.
• The points on a standing wave that have reached maximum oscillation do so from
constructive interference, and are called nodes.
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Appendix
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Waves and Vibrations: Waves
Key terms
• amplitude The maximum absolute value of some quantity that varies.
• boundary condition A set of restraints at the boundaries, used to solve a differential equation.
• boundary condition A set of restraints at the boundaries, used to solve a differential equation.
• compression to increase in density; the act of compressing, or the state of being compressed; compaction
• constructive interference Occurs when waves interfere with each other crest to crest and the waves are exactly in phase with
each other.
• constructive interference Occurs when waves interfere with each other crest to crest and the waves are exactly in phase with
each other.
• crest The ridge or top of a wave.
• destructive interference Occurs when waves interfere with each other crest to trough (peak to valley) and are exactly out of
phase with each other.
• destructive interference Occurs when waves interfere with each other crest to trough (peak to valley) and are exactly out of
phase with each other.
• direction of propagation The axis along which the wave travels.
• direction of propagation The axis along which the wave travels.
• energy A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²)
or the equivalent.
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Waves and Vibrations: Waves
• frequency The quotient of the number of times n a periodic phenomenon occurs over the time t in which it occurs: f = n / t.
• group velocity The propagation velocity of the envelope of a modulated travelling wave, which is considered as the propagation
velocity of information or energy contained in it.
• interference An effect caused by the superposition of two systems of waves, such as a distortion on a broadcast signal due to
atmospheric or other effects.
• interference An effect caused by the superposition of two systems of waves, such as a distortion on a broadcast signal due to
atmospheric or other effects.
• Longitudinal Running in the direction of the long axis of a body.
• medium The material or empty space through which signals, waves or forces pass.
• oscillate To swing back and forth, especially if with a regular rhythm.
• phase velocity The velocity of propagation of a pure sine wave of infinite extent and infinitesimal amplitude.
• photoelectric effects In photoelectric effects, electrons are emitted from matter (metals and non-metallic solids, liquids or gases)
as a consequence of their absorption of energy from electromagnetic radiation.
• plane wave A constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant
peak-to-peak amplitude normal to the phase velocity vector.
• power A measure of the rate of doing work or transferring energy.
• rarefaction a reduction in the density of a material, especially that of a fluid
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Waves and Vibrations: Waves
• refractive index The ratio of the speed of light in air or vacuum to that in another medium.
• resonance The increase in the amplitude of an oscillation of a system under the influence of a periodic force whose frequency
is close to that of the system's natural frequency.
• Restoring force If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back
toward equilibrium. The restoring force is a function only of position of the mass or particle. It is always directed back toward the
equilibrium position of the system.An example is the action of a spring. An idealized spring exerts a force that is proportional to
the amount of deformation of the spring from its equilibrium length, exerted in a direction to oppose the deformation. Pulling the
spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of
force can be determined by multiplying the spring constant of the spring by the amount of stretch.
• simple harmonic motion (SHM) — Oscillating motion (as of a pendulum) in which the acceleration of the oscillator has an equal
magnitude but opposite direction to the displacement of it from the equilibrium position.
• Snell's law A formula used to describe the relationship between the angles of incidence and refraction.
• speed of propagation The speed at which a wave moves through a medium.
• standing wave A wave form which occurs in a limited, fixed medium in such a way that the reflected wave coincides with the
produced wave. A common example is the vibration of the strings on a musical stringed instrument.
• superposition The summing of two or more field contributions occupying the same space.
• superposition The summing of two or more field contributions occupying the same space.
• transverse wave Any wave in which the direction of disturbance is perpendicular to the direction of travel.
• transverse wave Any wave in which the direction of disturbance is perpendicular to the direction of travel.
• transverse wave Any wave in which the direction of disturbance is perpendicular to the direction of travel.
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Waves and Vibrations: Waves
• transverse wave Any wave in which the direction of disturbance is perpendicular to the direction of travel.
• trough A long, narrow depression between waves or ridges.
• ultrasound Sound with a frequency greater than the upper limit of human hearing; approximately 20 kilohertz.
• wave A moving disturbance in the energy level of a field.
• wave equation An important second-order linear partial differential equation for the description of waves such as sound waves,
light waves, and water waves.
• wave speed The absolute value of the velocity at which the phase of any one frequency component of the wave travels.
• wavelength The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the
next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
• wavelength The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the
next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
• work A measure of energy expended in moving an object; most commonly, force times displacement. No work is done if the
object does not move.
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Waves and Vibrations: Waves
Wave motion
The point along the axis is analogous to the floating ball at sea. We notice that while it moves up and down it does not move in the direction of the wave's
propagation.
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Waves and Vibrations: Waves
Transverse Wave With a Fixed End Point
A transverse wave that is fixed at the end point. The reflected wave is inverted.
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Connexions. "Transverse Waves - Grade 10." CC BY 3.0 http://cnx.org/content/m32635/latest/ View on Boundless.com
Waves and Vibrations: Waves
Standing Waves
Standing waves in a string, the fundamental mode and the first six overtones.
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Waves and Vibrations: Waves
Wavelength and Amplitude
The wavelength is the distance between adjacent crests. The amplitude is the 1/2 the distance from crest to trough.
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Waves and Vibrations: Waves
Fixed End Reflection
When a transverse wave meets a fixed end, the wave is reflected, but inverted.
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Connexions. "Transverse Waves - Grade 10." CC BY 3.0 http://cnx.org/content/m32635/latest/ View on Boundless.com
Waves and Vibrations: Waves
Frequencies of different sine waves.
The red wave has a low frequency sine there is very little repetition of cycles. Conversely we say that the purple wave has a high frequency. Note that
time increases along the horizontal.
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Waves and Vibrations: Waves
The Wave Equation
A brief introduction to the wave equation, discussing wave velocity, frequency, wavelength, and period.
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Waves and Vibrations: Waves
Water waves
Surface waves in water
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Waves and Vibrations: Waves
Water waves
The motion water waves causes particles to follow clockwise circular motion. This is a result of the wave having both transverse and longitudinal
properties.
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Waves and Vibrations: Waves
Standing Wave on a String
This is what a standing wave would look like if you were to slow it down. The wave is caused by an incident wave on a string being reflected and then
traveling back in the direction it came from. The two waves then meet and interfere with each other causing this phenomenon.
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Waves and Vibrations: Waves
Two Strings With Different Density
Two strings with different density are connected and driven by an external driving force.
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Connexions. "Reflection and Transmission of Mechanical Waves." CC BY 3.0 http://cnx.org/content/m12794/latest/ View on Boundless.com
Waves and Vibrations: Waves
Harmonic Waves
Harmonic waves are described by sinusoidal functions. The wavelength is equal to linear distance between repetitions of transverse disturbance or
phase.
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Connexions. "Transverse harmonic waves." CC BY 3.0 http://cnx.org/content/m15992/latest/ View on Boundless.com
Waves and Vibrations: Waves
Two Types of Waves: Longitudinal vs. Transverse
Even ocean waves!
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Waves and Vibrations: Waves
Figure 1
In transverse waves, the media the wave is traveling in moves perpendicular to the direction of the wave.
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Connexions. "Transverse Waves - Grade 10." CC BY 3.0 http://cnx.org/content/m32635/latest/ View on Boundless.com
Waves and Vibrations: Waves
Plane wave
We see a wave propagating in the direction of the phase velocity. The wave can be thought to be made up of planes orthogonal to the direction of the
phase velocity.
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Waves and Vibrations: Waves
Wave Interference
A brief introduction to constructive and destructive wave interference and the principle of superposition.
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Waves and Vibrations: Waves
Fig 2
This shows a wave with the group velocity and phase velocity going in different directions. (The group velocity is positive and the phase velocity is
negative. )
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Waves and Vibrations: Waves
Earthquake Destruction
The destructive effect of an earthquake is palpable evidence of the energy carried in these waves. The Richter scale rating of earthquakes is related to
both their amplitude and the energy they carry.
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Waves and Vibrations: Waves
Two Types of Waves: Longitudinal vs. Transverse
Even ocean waves!
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Waves and Vibrations: Waves
Constructive Interference
Pure constructive interference of two identical waves produces one with twice the amplitude, but the same wavelength.
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Connexions. "Superposition and Interference." CC BY 3.0 http://cnx.org/content/m42249/latest/ View on Boundless.com
Waves and Vibrations: Waves
Refraction in Water
An object (in this case a pencil) partially immersed in water looks bent due to refraction: the light waves from X change direction and so seem to originate
at Y. (More accurately, for any angle of view, Y should be vertically above X, and the pencil should appear shorter, not longer as shown. )
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Waves and Vibrations: Waves
Standing Wave
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).
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Waves and Vibrations: Waves
Electromagnetic Wave
Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D diagram shows a
plane linearly polarized wave propagating from left to right.
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Waves and Vibrations: Waves
Transverse Wave With a Free End
When a transverse wave meets a free end, it is reflected.
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Connexions. "Transverse Waves - Grade 10." CC BY 3.0 http://cnx.org/content/m32635/latest/ View on Boundless.com
Waves and Vibrations: Waves
Wave Equation in Two Dimensions
A solution of the wave equation in two dimensions with a zero-displacement boundary condition along the entire outer edge.
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Waves and Vibrations: Waves
Transverse Wave
Diagram of a transverse wave. The wave motion moves perpendicular to the medium it is traveling in.
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Waves and Vibrations: Waves
Complex Pattern of Waves
These waves result from the superposition of several waves from different sources, producing a complex pattern.
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Connexions. "Superposition and Interference." CC BY 3.0 http://cnx.org/content/m42249/latest/ View on Boundless.com
Waves and Vibrations: Waves
Resonance
A brief overview of resonance, targeted toward introductory physics students.
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Waves and Vibrations: Waves
Longitudinal Waves
A compressed Slinky is an example of a longitudinal wave. The wave propagates in the same direction of oscillation.
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Waves and Vibrations: Waves
Sine Wave
The direction of propagation of this wave is along the t axis.
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Waves and Vibrations: Waves
Water Wave
Waves that are more massive or have a greater velocity transport more energy.
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Waves and Vibrations: Waves
Partial Transmittance and Partial Reflectance
A wave experiences partial transmittance and partial reflectance when the medium through which it travels suddenly changes.
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Waves and Vibrations: Waves
Superposition of Non-Identical Waves
Superposition of non-identical waves exhibits both constructive and destructive interference.
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Connexions. "Superposition and Interference." CC BY 3.0 http://cnx.org/content/m42249/latest/ View on Boundless.com
Waves and Vibrations: Waves
Figure 2
Peaks are the top most points of the waves and troughs are the bottom, or valleys of the waves.
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Waves and Vibrations: Waves
Free End Reflection
The wave is reflected, but unlike a transverse wave with a fixed end, it is not inverted.
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Waves and Vibrations: Waves
Intensity Pattern
Intensity pattern formed on a screen by diffraction from a square aperture.
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Waves and Vibrations: Waves
A wave
A) does not move mass in the direction of propagation; it transfers energy
B) does not move energy in the direction of propagation; it transfers mass
C) transfers both energy and mass in the direction of propagation
D) neither move energy nor mass in the direction of propagation
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Waves and Vibrations: Waves
A wave
A) does not move mass in the direction of propagation; it transfers energy
B) does not move energy in the direction of propagation; it transfers mass
C) transfers both energy and mass in the direction of propagation
D) neither move energy nor mass in the direction of propagation
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Waves and Vibrations: Waves
Depending on the direction of its oscillation, the wave can be
A) transverse or longitudinal
B) linear or circular
C) transverse or linear
D) circular or
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Waves and Vibrations: Waves
Depending on the direction of its oscillation, the wave can be
A) transverse or longitudinal
B) linear or circular
C) transverse or linear
D) circular or
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Waves and Vibrations: Waves
The following are examples of the transverse wave:
A) seismic waves and sound waves
B) seismic waves and the motion of the electric and magnetic fields in an
electromagnetic plane waves
C) pressure waves and the motion of the electric and magnetic fields in
an electromagnetic plane waves
D) pressure waves such as sound waves
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Waves and Vibrations: Waves
The following are examples of the transverse wave:
A) seismic waves and sound waves
B) seismic waves and the motion of the electric and magnetic fields in an
electromagnetic plane waves
C) pressure waves and the motion of the electric and magnetic fields in
an electromagnetic plane waves
D) pressure waves such as sound waves
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Waves and Vibrations: Waves
Transverse waves propagate through media
A) in the direction of energy transfer
B) against the direction of energy transfer
C) propagate through media orthogonally to the direction of energy
transfer
D) independently of the direction of energy transfer
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Waves and Vibrations: Waves
Transverse waves propagate through media
A) in the direction of energy transfer
B) against the direction of energy transfer
C) propagate through media orthogonally to the direction of energy
transfer
D) independently of the direction of energy transfer
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Waves and Vibrations: Waves
Longitudinal waves
A) oscillate in the direction of propagation and displace mass
B) oscillate perpendicular to the direction of propagation and do not
displace mass
C) oscillate in the direction of propagation and do not displace mass
D) oscillate perpendicular to the direction of propagation and displace
mass
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Waves and Vibrations: Waves
Longitudinal waves
A) oscillate in the direction of propagation and displace mass
B) oscillate perpendicular to the direction of propagation and do not
displace mass
C) oscillate in the direction of propagation and do not displace mass
D) oscillate perpendicular to the direction of propagation and displace
mass
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Waves and Vibrations: Waves
The following are examples of the longitudinal wave:
A) pressure waves with the exception of sound waves
B) pressure waves such as sound waves
C) seismic waves
D) seismic waves and sound waves
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Waves and Vibrations: Waves
The following are examples of the longitudinal wave:
A) pressure waves with the exception of sound waves
B) pressure waves such as sound waves
C) seismic waves
D) seismic waves and sound waves
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Waves and Vibrations: Waves
The particles which make up a water wave move in
A) linear paths
B) both transverse and longitudinal paths
C) both circular and linear paths
D) circular paths
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Waves and Vibrations: Waves
The particles which make up a water wave move in
A) linear paths
B) both transverse and longitudinal paths
C) both circular and linear paths
D) circular paths
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Waves and Vibrations: Waves
The uniqueness of water waves is found in the observation that
they comprise
A) longitudinal wave motion
B) transverse wave motion
C) transverse and circular wave motion
D) both transverse and longitudinal wave motion
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Waves and Vibrations: Waves
The uniqueness of water waves is found in the observation that
they comprise
A) longitudinal wave motion
B) transverse wave motion
C) transverse and circular wave motion
D) both transverse and longitudinal wave motion
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Waves and Vibrations: Waves
The solution of the the wave equation for a traveling wave is the
A) left traveling function
B) right traveling function
C) derivative of a left traveling function and a right traveling function
D) sum of a left traveling function and a right traveling function
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Waves and Vibrations: Waves
The solution of the the wave equation for a traveling wave is the
A) left traveling function
B) right traveling function
C) derivative of a left traveling function and a right traveling function
D) sum of a left traveling function and a right traveling function
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Waves and Vibrations: Waves
The amount of energy in a wave is
A) directly proportional to its amplitude
B) directly proportional to its amplitude squared
C) inversely proportional to its amplitude squared
D) inversely proportional to its amplitude
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Waves and Vibrations: Waves
The amount of energy in a wave is
A) directly proportional to its amplitude
B) directly proportional to its amplitude squared
C) inversely proportional to its amplitude squared
D) inversely proportional to its amplitude
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Waves and Vibrations: Waves
Major characteristic properties of waves include
A) frequency
B) wavelength
C) All of these answers
D) amplitude
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Waves and Vibrations: Waves
Major characteristic properties of waves include
A) frequency
B) wavelength
C) All of these answers
D) amplitude
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Waves and Vibrations: Waves
The group velocity is the velocity with which the
A) phase of the wave propagates in space
B) velocity with which the envelope of the wave propagates through
space
C) frequency component of the wave travels
D) group of waves travel
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Waves and Vibrations: Waves
The group velocity is the velocity with which the
A) phase of the wave propagates in space
B) velocity with which the envelope of the wave propagates through
space
C) frequency component of the wave travels
D) group of waves travel
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Waves and Vibrations: Waves
Waves that transfer more energy are
A) less massive and have greater velocities
B) more massive and have greater velocities
C) less massive and have smaller velocities
D) more massive and have smaller velocities
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Waves and Vibrations: Waves
Waves that transfer more energy are
A) less massive and have greater velocities
B) more massive and have greater velocities
C) less massive and have smaller velocities
D) more massive and have smaller velocities
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Waves and Vibrations: Waves
Energy of a wave is transported
A) opposite to the direction of the waves transportation
B) independently of the direction of the waves transportation
C) perpendicular to the direction of the waves transportation
D) in the direction of the waves transportation
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Waves and Vibrations: Waves
Energy of a wave is transported
A) opposite to the direction of the waves transportation
B) independently of the direction of the waves transportation
C) perpendicular to the direction of the waves transportation
D) in the direction of the waves transportation
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Waves and Vibrations: Waves
The superposition of two identical waves that arrive at the same
point exactly in phase corresponds to the
A) constructive interference with a wave that has twice the amplitude of
the individual waves
B) destructive interference with a wave that has twice the amplitude of
the individual waves
C) destructive interference with a wave that has zero amplitude
D) constructive interference with a wave that has zero amplitude
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Waves and Vibrations: Waves
The superposition of two identical waves that arrive at the same
point exactly in phase corresponds to the
A) constructive interference with a wave that has twice the amplitude of
the individual waves
B) destructive interference with a wave that has twice the amplitude of
the individual waves
C) destructive interference with a wave that has zero amplitude
D) constructive interference with a wave that has zero amplitude
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Waves and Vibrations: Waves
The waves superimpose themselves on one another when they
A) arrive to different points
B) are identical
C) have zero amplitude
D) arrive at the same point
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Waves and Vibrations: Waves
The waves superimpose themselves on one another when they
A) arrive to different points
B) are identical
C) have zero amplitude
D) arrive at the same point
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Waves and Vibrations: Waves
When the medium through which a wave travels suddenly
changes, the wave often experiences
A) absolute transmission through the interface
B) absolute refection by the interface
C) partial transmission and partial refection at the interface
D) frequency doubling
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Waves and Vibrations: Waves
When the medium through which a wave travels suddenly
changes, the wave often experiences
A) absolute transmission through the interface
B) absolute refection by the interface
C) partial transmission and partial refection at the interface
D) frequency doubling
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Waves and Vibrations: Waves
Transmission is a wave phenomenon that
A) permits the passage of wave with some or none of the incident wave
being absorbed
B) changes the direction of a wavefront at an interface between two
different media
C) blocks the passage of wave with all the incident wave being absorbed
D) permits the passage of wave with its frequency being doubled
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Waves and Vibrations: Waves
Transmission is a wave phenomenon that
A) permits the passage of wave with some or none of the incident wave
being absorbed
B) changes the direction of a wavefront at an interface between two
different media
C) blocks the passage of wave with all the incident wave being absorbed
D) permits the passage of wave with its frequency being doubled
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Waves and Vibrations: Waves
A standing wave is one in which two waves superimpose to
produce a wave that
A) varies in amplitude but does not propagate
B) varies in amplitude and propagates
C) does not vary in amplitude and does not propagate
D) does not vary in amplitude and propagates
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Waves and Vibrations: Waves
A standing wave is one in which two waves superimpose to
produce a wave that
A) varies in amplitude but does not propagate
B) varies in amplitude and propagates
C) does not vary in amplitude and does not propagate
D) does not vary in amplitude and propagates
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Waves and Vibrations: Waves
An antinode is
A) the location of minimum amplitude of a standing wave
B) point of no motion
C) the location of maximum amplitude of a standing wave
D) point of minimum motion
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Waves and Vibrations: Waves
An antinode is
A) the location of minimum amplitude of a standing wave
B) point of no motion
C) the location of maximum amplitude of a standing wave
D) point of minimum motion
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Waves and Vibrations: Waves
During refraction,
A) the phase velocity of the wave is changed, but its frequency remains
constant
B) both the phase velocity of the wave and frequency remain constant
C) both the phase velocity of the wave and frequency are changed
D) the phase velocity of the wave remains constant, but its frequency is
changed
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Waves and Vibrations: Waves
During refraction,
A) the phase velocity of the wave is changed, but its frequency remains
constant
B) both the phase velocity of the wave and frequency remain constant
C) both the phase velocity of the wave and frequency are changed
D) the phase velocity of the wave remains constant, but its frequency is
changed
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Waves and Vibrations: Waves
In optics, refraction is a phenomenon that occurs when waves
travel from a medium with a given refractive index to a medium
with another at an oblique angle
A) another refractive index at an oblique angle
B) identical refractive index at an oblique angle
C) identical refractive index at a right angle
D) another refractive index at a right angle
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Waves and Vibrations: Waves
In optics, refraction is a phenomenon that occurs when waves
travel from a medium with a given refractive index to a medium
with another at an oblique angle
A) another refractive index at an oblique angle
B) identical refractive index at an oblique angle
C) identical refractive index at a right angle
D) another refractive index at a right angle
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Waves and Vibrations: Waves
Diffraction effects are generally most pronounced for waves
whose wavelengths are
A) very small
B) very large
C) totally different from the dimensions of the diffracting objects
D) roughly similar to the dimensions of the diffracting objects
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Waves and Vibrations: Waves
Diffraction effects are generally most pronounced for waves
whose wavelengths are
A) very small
B) very large
C) totally different from the dimensions of the diffracting objects
D) roughly similar to the dimensions of the diffracting objects
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Waves and Vibrations: Waves
In classical physics, the diffraction phenomenon is described as
the
A) bending of waves around large obstacles and the spreading out of
waves past small openings
B) bending of waves around small obstacles and the spreading out of
waves past small openings
C) bending of waves around large obstacles and the spreading out of
waves past large openings
D) bending of waves around small obstacles and the spreading out of
waves past large openings
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Waves and Vibrations: Waves
In classical physics, the diffraction phenomenon is described as
the
A) bending of waves around large obstacles and the spreading out of
waves past small openings
B) bending of waves around small obstacles and the spreading out of
waves past small openings
C) bending of waves around large obstacles and the spreading out of
waves past large openings
D) bending of waves around small obstacles and the spreading out of
waves past large openings
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Waves and Vibrations: Waves
A standing wave occurs when
A) a transverse wave meets a fixed end
B) a transverse wave meets a free end
C) an incident wave meets a reflected wave on a string
D) an incident wave is reflected
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Waves and Vibrations: Waves
A standing wave occurs when
A) a transverse wave meets a fixed end
B) a transverse wave meets a free end
C) an incident wave meets a reflected wave on a string
D) an incident wave is reflected
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Waves and Vibrations: Waves
Nodes are points
A) that remain flat due to the destructive interference
B) that remain flat due to the constructive interference
C) with maximum oscillation due to the constructive interference
D) with maximum oscillation due to the destructive interference
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Waves and Vibrations: Waves
Nodes are points
A) that remain flat due to the destructive interference
B) that remain flat due to the constructive interference
C) with maximum oscillation due to the constructive interference
D) with maximum oscillation due to the destructive interference
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Waves and Vibrations: Waves
In a transverse wave, the wave direction is
A) parallel the direction that the string oscillates in
B) perpendicular the direction that the string oscillates in
C) coincides the direction that the string oscillates in
D) does not depend on the direction that the string oscillates in
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Waves and Vibrations: Waves
In a transverse wave, the wave direction is
A) parallel the direction that the string oscillates in
B) perpendicular the direction that the string oscillates in
C) coincides the direction that the string oscillates in
D) does not depend on the direction that the string oscillates in
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Waves and Vibrations: Waves
The speed of a wave on a string can be found by
A) multiplying the wavelength by the period
B) dividing the wavelength by the frequency
C) multiplying the frequency by the period
D) multiplying the wavelength by the frequency
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Waves and Vibrations: Waves
The speed of a wave on a string can be found by
A) multiplying the wavelength by the period
B) dividing the wavelength by the frequency
C) multiplying the frequency by the period
D) multiplying the wavelength by the frequency
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Waves and Vibrations: Waves
A standing wave occurs when
A) an incident wave meets a reflected wave on a string
B) a transverse wave in string meets one end
C) a transverse wave is reflected
D) a reflected wave meets another end
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Waves and Vibrations: Waves
A standing wave occurs when
A) an incident wave meets a reflected wave on a string
B) a transverse wave in string meets one end
C) a transverse wave is reflected
D) a reflected wave meets another end
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Waves and Vibrations: Waves
When transverse waves in strings meet one end, they are
A) diffracted
B) retracted
C) reduced
D) reflected
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Waves and Vibrations: Waves
When transverse waves in strings meet one end, they are
A) diffracted
B) retracted
C) reduced
D) reflected
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Waves and Vibrations: Waves
The points in a standing wave that appear to remain flat and do
not move are called
A) antinodes
B) nodes
C) reflected points
D) incident points
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Waves and Vibrations: Waves
The points in a standing wave that appear to remain flat and do
not move are called
A) antinodes
B) nodes
C) reflected points
D) incident points
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Waves and Vibrations: Waves
Attribution
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• Wikipedia. "Group velocity." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Group_velocity
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• Wikipedia. "Frequency." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Frequency
• Wikipedia. "Frequency." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Frequency
• Wiktionary. "frequency." CC BY-SA 3.0 http://en.wiktionary.org/wiki/frequency
• Wiktionary. "wavelength." CC BY-SA 3.0 http://en.wiktionary.org/wiki/wavelength
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• Wiktionary. "wave." CC BY-SA 3.0 http://en.wiktionary.org/wiki/wave
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• Wikipedia. "Waves." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Waves
• Wikipedia. "Wave power." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Wave_power
• Wikipedia. "Wave power." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Wave_power
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Waves and Vibrations: Waves
• Wikipedia. "Wave power." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Wave_power
• Wiktionary. "phase velocity." CC BY-SA 3.0 http://en.wiktionary.org/wiki/phase+velocity
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Waves and Vibrations: Waves
• Wiktionary. "refractive index." CC BY-SA 3.0 http://en.wiktionary.org/wiki/refractive+index
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Waves and Vibrations: Waves
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/destructive-interference
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/constructive-interference
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• Wiktionary. "wavelength." CC BY-SA 3.0 http://en.wiktionary.org/wiki/wavelength
• Wiktionary. "trough." CC BY-SA 3.0 http://en.wiktionary.org/wiki/trough
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• Wikipedia. "Vibrating string." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Vibrating_string
• Wiktionary. "oscillate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/oscillate
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Waves and Vibrations: Waves
• Wiktionary. "transverse wave." CC BY-SA 3.0 http://en.wiktionary.org/wiki/transverse+wave
• Connexions. "Transverse Waves - Grade 10." CC BY 3.0 http://cnx.org/content/m32635/latest/
• Wikipedia. "Vibrating string." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Vibrating_string
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• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/constructive-interference
• Wiktionary. "transverse wave." CC BY-SA 3.0 http://en.wiktionary.org/wiki/transverse+wave
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