Waves and Vibrations
Vibration - a movement to and fro. An oscillation
Period - time taken for one complete cycle or
Oscillation. Period is represented by the
symbol T and is measured in seconds.
- time for a “to-and-fro” movement
Note for a pendulum;
θ
length
mass
T, the period, is independent of the mass, m, of the
bob or the angle, θ.
The period is dependent on the length, l, and the
acceleration due to gravity, g.
The exact relationship is
T = 2π
Conceptual Physics – 3rd Edition – Paul Hewitt
l
g
Chapter 25 – Vibrations and Waves
Page 1 of 7
This curve depicts a wave.
+ve
Crest
Amplitude
Trough
Displacement
Wavelength
-ve
Displacements are measured from the mean position.
It is a series of crests and troughs.
Wavelength (λ) is the distance from one crest to
another crest, more generally the distance
between points in phase.
λ is measured in metres.
Frequency (f) is the number of to-and-fro vibrations
in a given time. f is measured in oscillations,
cycles per second or hertz.
Amplitude is the distance of the maximum
displacement point of the wave from the mean
position. Amplitude is measured in metres.
1
N.B. frequency =
period
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 2 of 7
Wave Motion – is a transfer of energy from one
point to another with no net transfer
of matter.
Wave Equation
v = fλ
where; v = speed or velocity of the wave (in m·s-1)
f = frequency in hertz (Hz)
λ = wavelength in metres.
Transverse Wave
This is a wave where the motion of the particles
or medium is perpendicular to the direction of travel.
v
It consists of a series of crests and troughs.
An example can be shown using a skipping rope
or a slinky spring.
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 3 of 7
Longitudinal Waves
The particles of the medium move along the
direction of the wave. The wave consists of a series
of compressions and rarefactions.
C R C R C R C
R
R = Rarefaction
C = Compression
λ
Particle
Vibration
N.B. In both of the wave types the energy is
transferred and not the matter.
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 4 of 7
Interference
Wave addition is the super-positions of wave forms
e.g. Crest + Crest
+
=
Constructive
Interference
Trough + Trough
+
=
Crest + Trough
+
=
Destructive
Interference
When waves overlap interference is produced.
Watching the sea waves being reflected from the
shore will illustrate wave interference
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 5 of 7
Standing Waves
Adding an incident and a reflected wave, you
produce interference between these two waves to
give a standing (stationary) wave.
Points of maximum displacement are called
anti nodes.
Points of no displacement are called nodes.
N
A
N
A
N
A
N
A
N
A
N
N = Nodes (points of no movement) i.e. appear
stationary.
A = Anti nodes (points of maximum movement).
The wave appears stationary because its nodes
and anti nodes do not move.
Note: Only specific frequencies will yield a
standing wave in a given medium.
- by shaking a spring
different frequencies
a variety of standing waves
can be produced.
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 6 of 7
The Doppler Effect.
If the source is stationary;
A
B
Observers at A and B
receive the same number of
waves per second(wave
frequency is the same).
If the source is moving;
A
Observer A receives fewer
waves per second than
B observer B. Wave frequency
is increased for observer B
and decreased for observer A
The Doppler Effect is the change in the apparent
frequency due to either the motion of the source or
the receiver or both. For example
1) water waves
2) changing sound frequency - a passing ambulance
3) radar waves – police radar
4) astronomy – red shift due to the motion of galaxies.
Conceptual Physics – 3rd Edition – Paul Hewitt
Chapter 25 – Vibrations and Waves
Page 7 of 7