Download 4.4 Wave Characteristics

4.4 Wave Characteristics
4.4.2
 A wave is a disturbance travelling
through a medium. In a wave, there is a
transmission of ENERGY, but no
transmission of MATTER.
 A wave is a means by which energy is
transferred between two points in a
medium without any net transfer of
the medium itself.
 Medium - The substance or object in
which the wave is travelling.
 When a wave travels in a medium parts of
the medium do not end up at different
places
 The energy of the source of the wave is
carried to different parts of the medium by the wave.
 A wave travels along its medium, but the individual particles just move up and down.
4.4.1
 A pulse is a short burst of wave energy.
 In a continuous wave, energy is being continuously transmitted by the wave, and the wave profile
travels onward with characteristic wave velocity v.
 All types of traveling waves transport energy.
 Study of a single wave pulse shows that it is begun with a vibration and transmitted through internal
forces in the medium.
 Continuous waves start with vibrations too. If the vibration is SHM, then the wave will be sinusoidal.
Types of Waves
 Waves can be described as transverse or longitudinal.
 In a transverse wave the vibration (oscillation) of particles is at right angles to the direction of energy
transfer. Transverse waves cannot move through a gas.
 Examples
 In a longitudinal wave the vibration of particles is in the same plane as the direction of energy transfer.
 Examples:
 The motion of particles in a wave can either be perpendicular to the wave direction (transverse)
or parallel to it (longitudinal).
 Sound waves are longitudinal waves. Light waves are transverse waves.
4.4.3
 Think about the wave that are constantly hitting a beach. Each wave has a crest and trough. Imagine
you are in a helicopter. If you look down you will see wavefronts.
 Lines perpendicular to the wave fronts are called rays; they point in
the direction of propagation of the wave.
 Two- or three-dimensional waves can be represented by wave
fronts, which are curves of surfaces where all the waves have the
same phase.
 Lines perpendicular to the wave fronts are called rays; they point in
the direction of propagation of the wave and the direction energy is
traveling.
 If a wave is able to spread out three-dimensionally from its source,
and the medium is uniform, the wave is spherical.
4.4.5
 Wave characteristics:
 Amplitude, A
 Wavelength, λ
 Frequency f and period T
 Wave velocity
 Describing Waves
 Crest and trough: Points on the wave where particles are oscillating at maximum positive and
negative displacement.
 Rarefaction and compression: Areas in a longitudinal wave where particles are far apart (lower
than normal density) and close together (higher than normal density).
 Many times longitudinal wave are graphed to better analyze them. Notice that the high pressure
corresponds to a compression and low pressure corresponds to a rarefaction.
4.4.6
 Displacement (s) is the distance that any particle is away from its equilibrium position at an instance.
Measured in meters.
 Amplitude (A, a) This is the maximum displacement of a particle from its equilibrium position.
Measured in meters.
 Period (T) This is the time that it takes a particle to make one complete oscillation. Measured in
seconds.
 Frequency (f) This is the number of oscillations made per second by a particle. The SI unit of
frequency is the hertz -Hz. (1 Hz is 1 oscillation per second). Clearly then, f = 1/T
 Wavelength () This is the distance along the medium between two successive particles that have the
same displacement and the same phase of motion. Measured in meters.
 Wave Speed (v, c) This is the speed with which energy is carried in the medium by the wave.
Measured in ms-1
Example Problem 1
 If the waves in the ocean are timed so that they come to shore every 1.74 seconds, what is the
frequency of these wave?
 Answer: 0.575Hz
Example Problem 2
 A radio wave has a frequency of 2 MHz. Calculate the time period
between successive waves.
 Answer: 5x10-7s
Wave Characteristics
 Amplitude.
 Height of a wave from origin to a peak/crest.
 Affects brightness and intensity.
 Wavelength.
 Distance from crest to crest. Distance for one full cycle.
 Visible light: 400-750nm.
 Period
 time that it takes to complete a full cycle.
 Measured in seconds
 Frequency.
 number of cycles per second.
 Measured in hertz(Hz)
 High frequency = high energy
 Speed of light
 Speed of light a constant: 3.00 X 108 m/s.
 Frequency and Wavelength related by the equation:  = c / 
4.4.7
 Split up into groups of 2.
 Draw one wave with wavelength 2 cm
 Draw second wave with wavelength 4 cm.
 Draw a third wave with wavelength 8cme.
 Draw 3 more waves with the same wavelengths as the first set but with an amplitude of 6 cm.
4.4.8
 There is a very simple relationship that links wave speed, wavelength, and frequency. It applies to all
waves. The time taken for one complete oscillation is the period of the wave, T.
 In this time, the wave pattern will have moved on by one wavelength, λ.
 This means that the speed of the wave must be given by
 V=d =λ since T= 1
 t T
f
 Then we get
Example 3
 A radio station broadcasts with a wavelength of 160m. If the velocity of the radio signal is 3 x 108m/s,
calculate the frequency of the wave.
 Answer: 1.88MHz
Example 4
 A water wave reaches the beach every 2.5 seconds. If it’s wavelength is 5m, calculate the speed of the
wave.
 Answer: 2m/s
Example 5
 A stone is thrown into a still water surface and creates a
wave. A small floating cork 2m away from the impact
point has the following displacement-time graph (time is
measured from the instant the stone hits the water).
 Determine:
 The amplitude
 The velocity
 The period of the wave
 The frequency of the wave
 The wavelength of the wave
 The time when the reaches its maximum vertical
height
4.4.9
The Electromagnetic Spectrum
 Electromagnetic waves are waves have a magnetic field oscillating in one dimension and an electric
field oscillating in another direction.
 They are transverse waves, however they are waves of fields and not matter. Because of this they can
propagate (travel) in a vacuum.
 EM properties
1) All EM waves share similar properties.
2) They all propagate by means of changing electric and magnetic fields.
3) They are all transverse in nature.
4) They all travel at the same speed in a vacuum. (3x108m/s = c)
 Electromagnetic waves
 Light is a form of Electromagnetic Radiation.
 EM Radiation has waves in the electric and magnetic fields
 Electromagnetic waves have two basic parts.
 electric field
 magnetic field
 The fields are perpendicular to each other.
 Many parts including:
 Gamma Rays (10-11 m)
 X-Rays (10-9 m)
 Ultra-violet (10-8
m)
 Visible (10-7 m)
 Infared (10-6 m)
 Microwave (10-2
m)
 TV/Radio (10-1
m)

 Visible Spectrum:
 ROY G BIV
 Red
 Orange
 Yellow
 Green
 Blue
 Indigo
 Violet
 Notice that
the speed of
the light is a
constant for any point of the spectrum. Ex Radio
EM Background
 James Maxwell helped to develop our understanding of EM waves.
 Used four equations to describe EM waves
 Showed EM waves travel at 2.998x108 m/s
 Showed that speed of EM waves is dependent on two constants, the permittivity of free space, ε0 and
the permeability of free space, µ0.
 The permittivity of free space, ε0 describes the electric characteristic of the wave.
 The permeability of free space, µ0 describes the magnetic characteristic of the wave.
 ε0 = 8.85 x 10-12 C2/Nm2
 µ0 = 4π x 10-7 m/A
 So….
 c = 1/(√ε0µ0)
 c = 1/(√8.85 x 10-1 x 4π x 10-7

= 2.9986 x 108 m/s

= 3 x 108 m/s