Homework
• SHM: Q2,3,4(a),6
• Deadline: Day 4
1
Wave propagation
Require a
medium to
transmit energy?
Examples
Mechanical
waves
Yes
Sound
waves
Waves in a
slinky spring
Electromagnetic
waves
No
Light
Radio waves
Transverse waves
Longitudinal waves
Vibrations are at right angles to Vibrations are along the
the direction of travel of the
direction of travel of the wave
wave
Direction of
vibration
Direction of
vibration
Direction of
travel of wave
Examples
Electromagnetic
waves, water
waves
Direction of
travel of wave
Examples Sound waves
Progressive / traveling
waves
A disturbance moving from
a source to surrounding places
Energy is transmitted
Stationary / standing
waves
Energy is localized
l
C
C
C
A
Resting
position
T
T
T
Amplitude A: maximum disturbance measured from the
resting position
Wavelength l: minimum distance in which a wave
repeat itself
Frequency f: number of waves produced in one second
Period T: time taken for one wave to be produced
(T = 1/f = 2p/w)
l
C
C
C
A
Resting
position
T
T
T
Wave speed v: distance traveled by a wave in one second.
(v = fl)
When waves travel along a string or spring, the wave speed is
given by v 
T

where T is the tension in the string or
spring and m is its mass per unit length.
This implies the wave speed can be increased if by stretching
the string or spring more.
l
C
C
C
A
Resting
position
T
T
T
Crest C: the peak of disturbance
Trough T: the bottom of disturbance
Note:
1. Speed of vibrating particles ≠ wave speed
4A
2. Average speed of vibrating particles =
.
T
Displacement – distance graph and
displacement – time graph
Displacement – distance graph shows the displacements
of all the particles on the wave at a certain time.
Displacement – time graph shows the displacement of
one particle at different times
Example 1
displacement / cm
travelling direction
A
4
0
B
5
D
C

10
15
20
distance / cm
4
(a) Find the amplitude, and the wavelength of the wave.
(b) If particle B performs 5 complete oscillations in 2 s,
find the frequency and the speed of the wave.
displacement / cm
Example 1
travelling direction
A
4
0
B
5
D
C

10
15
20
distance / cm
4
(c) At the instant shown, which of the particles A, B, C
or D, is/are
(i)
momentarily at rest,
(ii)
moving upwards, and
(iii)
moving downwards?
Phase difference
of
particles
in
a
wave
displacement
Direction of wave
P
Q
distance
Time
P
Q
0
At rest
Upward
¼T
Downward
At rest
½T
At rest
Downward
¾T
Upward
At rest
T
At rest
Upward
Phase difference
of
particles
in
a
wave
displacement
Direction of wave
P
Q
distance
P leads Q by ¼ T or 90o or p/2 radians
Phase difference of particles in a wave
displacement
P’
w
Q’
Direction of wave
P
Q
distance
Vectors P’ and Q’ are rotating in anticlockwise direction
with angular speed w where.
The projections of vectors P’ and Q’ on the axis of
displacement give the displacement time graphs of
particles P and Q.
Phase difference of P and Q is 90o or p / 2 radians.
P leads Q by 90o or p / 2 radians.