1. wave
A wave is a phenomenon in which energy is transferred through vibrations.
A wave carries energy away from the wave source.

2. Describing wave motion`
wave
The effect of rope waves can be seen by fixing one end of a rope by tying it around a rod and moving the other end up and down.
Similar effect for water waves
water is the medium through which energy transmits
a cork on the water surface bobs up and down as the wave passes
it does not travel forward with the wave

3. Describing wave motion`
water waves
Waves are produced by dipping either a
horizontal bar into the water to obtain plane waves
ball-ended dipper to obtain circular waves
up-and-down motion of bar
up-and-down motion of dipper
plane waves
circular waves
A motor fixed to the bar or dipper will cause it to move up and down to generate continuous waves.

4. `
Classwork Practice 1.
The diagram shows a ball floating in a tank of water.
Which diagram shows the movement of the ball when the wave passes?
[ ] D

5. finger dipping into water
Wavefronts `
Water waves are easily produced and observed.
By touching one point on the surface,
peaks of the waves form circles
waves move outwards from the source of disturbance
finger dipping into water
direction of travel
circular wavefronts
The imaginary line on wave that joins all points which have the same phase of vibration (e.g. all the crests of the water wave) is called the wavefront.

6. Wavefronts `
Plane waves are produced by touching the water surface with a wooden bar. The wavefront of plane waves are straight lines.
vibrating bar
direction of travel
plane wavefronts
The direction of travel of waves is always perpendicular to the wavefront.

7. pendulum bob tied to one end of a thread
Terms used to describe waves `
Some of the terms used to describe waves:
Amplitude (A/m)
Period (T/s)
Frequency (f/Hz)
pendulum bob tied to one end of a thread B A O
amplitude

8. Terms used to describe waves `
We make use of 2 types of graphs to describe the terms associated with wave motion.
Displacement-position graph
x-axis – positions of particles
y-axis – displacement of particles
Displacement-time graph
x-axis – time
y-axis – displacement of particular particle
Instantaneous picture of how much all particles at various positions have been displaced from their original rest positions
Instantaneous picture of how much all particles at various positions have been displaced from their original rest positions
Plot of displacement of a single particle over a continuous duration of time
Plot of displacement of a single particle over a continuous duration of time

9. Displacement-position graph `
Displacement made by each particle (m)
t = 1.6 s
t = 1.7 s
t = 1.8 s
t = 1.5 s
t = 1.2 s
t = 1.1 s
t = 1.9 s
t = 1.3 s
t = 1.4 s
t = 2.1 s
t = 2.6 s
t = 2.7 s
t = 2.8 s
t = 2.5 s
t = 2.4 s
t = 1.0 s
t = 2.2 s
t = 2.3 s
t = 2.0 s
t = 0.7 s
t = 0.3 s
t = 0.2 s
t = 0.9 s
t = 0.4 s
t = 0.1 s
t = 0.5 s
t = 0.6 s
t = 0.8 s
1.0 m
0.8 m
0.5 m
Central or rest position of undisturbed rope
Distance along rope (m)
- 0.5 m
- 0.8 m
- 1.0 m
Definitions :
Tells us how much each of all the particles along the rope (wave) has been displaced from their rest position at any instance of time
What do you observe about the motion of the 2 particles in blue?
Their maximum displacement from the rest position in either direction is 1 m (Amplitude)
They are always moving in the same direction with the same speed and having the same displacement from the rest position (in phase)

10. Displacement-position graph `
Displacement made by each particle (m)
t = 2.8 s
X, crest
Y, crest
1.0 m
0.8 m
0.5 m
Amplitude, A
Central or rest position of undisturbed rope
Amplitude, A
Distance along rope (m)
- 0.5 m
- 0.8 m
- 1.0 m
trough
Definitions :
Crests & troughs
These are the high & low points that characterise transverse waves only
Amplitude A
Maximum displacement from the rest position in either direction. SI unit is the metre (m)
Phase
2 points (e.g. X & Y) are in phase if they always move in the same direction with the same speed & have the same displacement from the rest position. Any 2 crests or troughs are in phase.

11. Displacement-position graph `
Displacement made by each particle (m)
t = 2.8 s λ
= 0.12 m
X, crest
Y, crest
1.0 m
0.8 m
0.5 m
0.13 m B
Amplitude, A
Central or rest position of undisturbed rope A
Amplitude, - A
Distance along rope (m)
0.01 m
- 0.5 m
- 0.8 m
- 1.0 m
trough
Definitions :
Wavelength λ
The shortest distance between any 2 points on a wave that are in phase. The 2 easiest points to choose for a distance of 1 wavelength are 2 successive crests or troughs. SI unit is the metre (m)
Frequency, f
The number of complete waves produced per second. From the figure above, there are 1½ complete waves.
If they are produced in 0.1 seconds, the frequency of the wave is
1.5 waves /0.1 seconds = 15 waves per second or 15 hertz (Hz)
Hertz is the SI unit for frequency.

12. ` Classwork Practice Classwork MCQ ` C 2.
The diagram shows a cross-section of a water wave. Which distance is the amplitude of the wave? E
[ ] C

13. ` Classwork Practice Class work MCQ ` D 3.
A long rope is stretched out on the floor. One end of the rope is then shaken. The graph shows the rope at a particular moment in time.
Which is the wavelength of the wave motion?
A 0.36 m C 0.8 m
B 0.6 m D 1.6 m [ ] D

14. `
Classwork Practice
4. Draw sketches of the displacement-distance graphs of the following waveforms.
Two waves having the same amplitude and speed but the wavelength of one is twice of the other
Two waves having the same speed and frequency but the amplitude of one is twice of the other
Displacement (m)
Wave 1
Wave 2
Displacement (m)
Wave 1
Wave 2
Distance (m)
Distance (m)
The wavelength of wave 1 is twice the wavelength of wave 2
The amplitude of wave 2 is twice the amplitude of wave 1

15. Displacement – position graph Displacement – time graph`
The plot of how the displacement of a single particle at a particular position changes over certain time duration.
Displacement of each particle (m)
t = 1.8 s
t = 1.9 s
t = 2.0 s
t = 1.7 s
t = 1.3 s
t = 1.2 s
t = 2.1 s
t = 1.5 s
t = 1.6 s
t = 2.4 s
t = 2.7 s
t = 2.8 s
t = 0.0 s
t = 2.6 s
t = 2.5 s
t = 2.3 s
t = 1.1 s
t = 2.2 s
t = 1.4 s
t = 0.4 s
t = 0.3 s
t = 0.1 s
t = 1.0 s
t = 0.5 s
t = 0.2 s
t = 0.9 s
t = 0.8 s
t = 0.6 s
t = 0.7 s
1.0 m
0.8 m
Displacement – position graph
0.5 m
Central or rest position of undisturbed rope
0.05 m
0.10 m
0.15 m
Distance along rope (m)
- 0.5 m
- 0.8 m
- 1.0 m
Displacement of particular particle (m)
1.0 m x x x x
0.8 m x
Displacement – time graph x x x
0.5 m x x x x x x x x x x x
0.5 s
1.0 s
1.5 s
2.0 s
2.5 s
Time (s)
- 0.5 m x x x x
- 0.8 m x x x x x x
- 1.0 m

16. Displacement-time graph `x x x
0.8 m x x x x x
0.5 m x x x x x x x x x x x
0.5 s
1.0 s
1.5 s
2.0 s
2.5 s
Time (s)
- 0.5 m x x x x
- 0.8 m x x x x x x
- 1.0 m
Amplitude, A
Maximum displacement from the rest position in either direction
Period, T
Time taken to produce one complete wave. S.I. unit is the second (s)
e.g. the particle is initially at rest at t = 0.1 s. It makes 1 complete oscillation and returns to the rest position at t = 1.3 s
Thus, this wave has a period of 1.2 s
Frequency, f
The number of complete waves produced per second. S.I units is Hz.
This implies that relation between period T and frequency f is, 1 / T
Thus the frequency of this wave is 1 / 1.2 = 0.83 Hz
Wave speed, v
Distance travelled by a wave in 1 second. S.I. unit is (ms-1)

17. ` Classwork Practice Class work MCQ ` B 5.
The diagram shows how displacement varies with time as a wave passes a fixed point.
What is the frequency of this wave?
A 0.25 Hz C 1.0 Hz
B 0.50 Hz D 2.0 Hz [ ] B

18. `
Classwork Practice
6. Draw sketches of the displacement-time graphs of the following waveforms
Wave A has the same speed as wave B but its period and amplitude is half that of B
Displacement (m)
Wave B
Wave A
Time (s)

19. up-and-down motion of dipper
Wave Speed
In a time of 1 period (T), a crest will have moved a distance of one wavelength (λ).
Therefore the speed of the wave, v is given by
But since
Therefore
up-and-down motion of dipper
direction of travel
circular wavefronts

20. `
Classwork Practice
7. A ripple tank was used to generate water waves of wavelength 0.10 m.
If the dipper of the ripple tank vibrates at a frequency of 30 Hz, what is the speed of the water waves?
Given Wavelength, λ = 0.10 m
Frequency, f = 30 Hz
From v = fλ
Wave speed v = 0.10 ×30
= 3.0 ms-1 (2 s.f.)
If the frequency is adjusted to 50 Hz, what will the new wavelength of the waves be, assuming that the wave speed remains unchanged?
New frequency f’ = 50 Hz
From v = f’λ’, where λ’ = new wavelength
New wavelength λ’ = v / f’
= 3.0 / 50
= 0.060m (2 s.f.)

21. coil vibrates up and down when shook up and down
Transverse and longitudinal waves
transverse waves
Waves which travel in a direction perpendicular to the direction of the vibrations.
coil vibrates up and down when shook up and down
direction of wave
wave moves this way
direction of the vibrations
one wavelength

22. Transverse and longitudinal waves
transverse waves
Identify the
Direction of vibration of particles along the wave
Direction of wave travel

23. Transverse and longitudinal waves
transverse waves
Identify the
Direction of vibration of particles along the wave
Direction of wave travel
Water waves, rope waves, light waves and other electro-magnetic waves are examples of transverse waves.

24. coil vibrates forward and backward when pushed in and out
Transverse and longitudinal waves
longitudinal waves
Waves which travel in a direction parallel to the direction of the vibrations.
coil vibrates forward and backward when pushed in and out
wave moves this way

25. Transverse and longitudinal waves
Identify the
Direction of vibration of particles along the wave
Direction of wave travel
Sound wave is an example of longitudinal wave.

26. Transverse and longitudinal waves
Can you identify the distance of one wavelength?
coil vibrates forward and backward when pushed in and out
wave moves this way c r c r c r
one wavelength
compression is the part where particles are closest to one another
rarefaction is the part where particles are spread apart C R R R C λ

27. Distance along slinky (m)
Transverse and longitudinal waves
longitudinal waves
Rest position of particle
After some time … λ
0.50 m
1.00 m
1.50 m
Distance along slinky (m)
Displacement of each particle (m) x x
0.06 m x x x
0.05 m x x x λ
0.03 m x x x m x x m x x x m

28. Displacement – time graph
Transverse and longitudinal waves
longitudinal waves
t = 0.0 s
t = 1.8 s
t = 1.9 s
t = 1.6 s
t = 2.0 s
t = 1.7 s
t = 2.2 s
t = 2.5 s
t = 2.6 s
t = 2.4 s
t = 2.3 s
t = 1.5 s
t = 2.1 s
t = 1.4 s
t = 0.4 s
t = 0.5 s
t = 0.3 s
t = 0.2 s
t = 0.1 s
t = 0.6 s
t = 0.7 s
t = 1.1 s
t = 1.2 s
t = 1.3 s
t = 1.0 s
t = 0.8 s
t = 0.9 s
Displacement – time graph
Displacement of particular particle (m)
1.0 m x x
0.8 m x x x x
0.5 m x x x x x x x x x x x
0.5 s
1.0 s
1.5 s
2.0 s
2.5 s
Time (s)
- 0.5 m x x x x
- 0.8 m x x x x x x
- 1.0 m

29. Waves Amplitude, a Period, T Wavelength,  Frequency, f = 1/T
Speed, v = f 
defined using
classified as
Transverse
Longitudinal
consists of
consists of
Crest
Trough
Compression
Rarefaction
example
example
Water wave
Light wave
E.M. wave
Sound wave