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Introduction
What is Vibration?
A vibration can be defined as a back-and-forth motion
around a point of rest or, more generally, as a variation of
any physical property of a system around a reference
value.
Vibration refers to mechanical oscillations about an
equilibrium point. The oscillations may be periodic such as
the motion of a pendulum or random such as the
movement of a tire on a gravel road.
Types of vibration:
Free vibration occurs when a mechanical system is set off with an
initial input and then allowed to vibrate freely.
• Examples: Pulling a child back on a swing and then letting go
•The mechanical system will then vibrate at one or more of its
natural frequencies and damp down to zero.
Forced vibration is when an alternating force or motion is applied to
a mechanical system.
• Examples: Shaking washing machining due to an imbalance,
transportation vibration (caused by truck engine, springs, road, etc),
or the vibration of a building during an earthquake.
- Magnitude of the vibration is strongly dependent on the
behavior of the mechanical system
What is Wave?
A wave is a disturbance that propagates through space or
spacetime, transferring energy and momentum and
sometimes angular momentum.
OR
A disturbance (interruption) traveling through a medium
by which energy is transferred from one particle of the
medium to another without causing any permanent
displacement of the medium itself.
EXAMPLES APPLICATION OF WAVES
Concepts of Wave
•The fundamental essence of a wave is the transfer of
energy without the accompanying transfer of mass.
•In its most basic form, a wave is propagation of a
disturbance through a medium.
•The medium is a collection of particles that exist at
equilibrium positions – they are disturbed from these
positions, they will feel a restoring force – thus, the
particles are oscillators.
•In addition, these particles must interact with their
neighbours, so that a disturbance can be passed from one
particle to the next.
FORM OF WAVES:
Transverse waves cause the medium to move
perpendicular to the direction of the wave.
Longitudinal waves cause the medium to move
parallel to the direction of the wave.
Surface waves are both transverse waves and
longitudinal waves mixed in one medium.
Example: water waves, sound waves, seismic waves.
TYPES of waves:
• Electromagnetic waves do not require a medium to
travel (light, radio). Example: visible light, ultraviolet
light, radio waves, television waves, microwaves, x-rays
and radar waves
•Matter waves are produced by electrons and
particles. Example: electrons, protons, atom, molecules.
•Mechanical waves require a material medium to
travel (air, water, ropes).
WAVE MOTION
A wave pulse is a disturbance
that propagates through a
medium.
It transfers energy without
transferring matter; the energy
is a combination of kinetic and
potential energy.
Rythmic disturbance in both
space and time is called wave,
and the transfer of energy is said
to take place by means of wave
motion.
Describing Waves
A harmonic disturbance can set up a sinusoidal wave. The distance from crest
to crest, or trough to trough, is called the wavelength, λ.
Amplitude (A): maximum displacement
Wavelength ( λ): distance between points having the same phase
Frequency (f ): number of waves passing per second
Period (T ): time for one complete wave to pass
Relationship between wave speed (v), wavelength, period, and frequency:
Waves may be either:
a) Transverse
(displacement perpendicular to
direction of propagation)
b) Longitudinal
(displacement parallel to direction of
propagation).
EXAMPLE 1
The figure shows a sinusoidal wave traveling on a string in 100 m/s. Calculate the
a) Amplitude, A
Ans: 10m
b) Wavelength, λ
Ans: 16m
c) Frequency, f
Ans: 6.25 Hz
d) Period, T
Ans: 0.16s
Wave Properties
Superposition and Interference
When two or more waves travel
through the same medium at the
same time, they interfere in a process
called superposition.
At any time/point, the combined
waveform of two or more interfering
waves is given by the sum of the
displacements of the individual waves
at each point in the medium.
Wave Properties
If the combined wave is larger than the individual ones, the
interference is constructive; if smaller, it is destructive.
Wave Properties: Reflection
Whether or not a wave is inverted upon reflection depends on
whether the end is free to move or not.
Wave Properties: Refraction
When a wave enters a new medium, its speed usually changes, as the
properties of the new medium are different.
The direction of propagation changes also; this is called refraction.
Wave Properties: Dispersion and
Diffraction
If the speed of the wave depends on its wavelength, it exhibits
dispersion.
example of dispersion.
Diffraction – refers to the bending of waves around an edge of
an object and is not related to refraction.
Diffraction occurs when a wave passes through an opening that
is comparable in size to the wavelength; the waves will “bend”
around the edges of the opening.
Standing Waves
On a rope with one fixed end, it is possible to set up waves that do not
travel; they simply vibrate in place. These are called standing waves.
Some points on the wave remain stationary all the time; these are called nodes.
Others have the maximum displacement; these are called antinodes.
Standing Waves and Resonance
Adjacent nodes are separated by
half a wavelength, as are adjacent
antinodes.
When an integral number of
half-wavelengths fit on the rope,
the frequency is called the
resonant frequency.
EXERCISE
1. A 0.75 kg toy oscillating on a spring completes a cycle every 0.6s. What is the
frequency of this oscillation?
2. The frequency of a simple harmonic oscillator is doubled from 0.25Hz to 0.5Hz.
What is the change in its period?
3. A transverse wave has a wavelength of 0.5 m and a frequency of 20Hz. What is
the wave speed?
4. A longitudinal sound wave has a speed of 340m/s in air. If this wave produces a
tone with a frequency of 1000Hz, what is its wavelength?
5. The distance between two incoming wave crests is about 0.75m, and the time
arrival between the crests to be 1.6 s. What is the approximate speed of the
waves?