travelling waves

1. Topic 4.2
Travelling waves

2. Travelling Waves
There are two types of waves
and pulses that we encounter
in the physical world.

3. Transverse
In these waves the source that produces the wave
oscillates at right angles to the direction of travel of
the wave
It means that the particles of the medium through
which the wave travels also oscillates at right angle
to the direction of travel of the wave.

4. Direction of travel
of the wave
Direction of oscillation
of the particles
Transverse Wave

5. Longitudinal
In these waves the source that produces the
wave oscillates in the same direction as the
direction of travel of the wave
It means that the particle of the medium
through which the wave travels also
oscillates in the same direction as the
direction of travel of the wave.

6. Longitudinal Wave
Direction of travel
of the wave
Direction of oscillations
of the particles

7. Discrete Pulses and Continuous Waves
A single shake of a slinky will send a discrete
pulse down it
Shake the slinky up and down and a
continuous travelling wave travels down it
This applies to longitudinal waves too

10. Question:
•List 6 types of wave and classify them
according to the types you have just learnt.

12. Definitions
The following definitions are given in terms of the
particles that make up the medium through which
the wave travels.
For the slinky spring a particle would be a single
turn of the spring
For the water waves a particle would be a very
small part of the water.

13. What is a Wave?
A wave is a means by which energy is
transferred between two points in a medium
without any net transfer of the medium itself.

14. The 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.

15. Water waves however, can be a bit
disconcerting.
Waves at sea do not transport water but the
tides do.
Similarly, a wave on a lake does not
transport water but water can actually be
blown along by the wind.

16. Displacement
(s) is the distance that any particle
is away from its equilibrium position
at an instance
Measured in metres

17. Crest
This is a term coined from water
waves and refers to the points at
the maximum height of the wave.
It is the positive displacement
from equilibrium

18. Trough
A term coined from water waves
referring to the points at the lowest
part of the wave.
The negative displacement from
equilibrium.

19. Compression
This is a term used in connection with
longitudinal wave and refers to the region
where the particles of the medium are
"bunched up".
High density
High pressure

20. Rarefaction
A term used in connection with longitudinal
waves referring to the regions where the
particles are "stretched out".
Low density
Low pressure

21. Wavelength
(λ) This is the distance along the medium between
two successive particles that have the same
displacement and the same phase of motion.
Measured in metres

22. Amplitude
(A, a) This is the maximum displacement of a
particle from its equilibrium position
(It is also equal to the maximum
displacement of the source that produces the
wave).
Normally measured in metres

23. Period
(T) This is the time that it takes a particle to
make one complete oscillation
(It also equals the time for the source of the
wave to make one complete oscillation).
Measured in seconds

24. Frequency
(f) This is the number of oscillations made per
second by a particle
(It is also equal to the number of oscillations made
per second by the source of the wave)
The SI unit of frequency is the Hertz - Hz. (1 Hz is
1 oscillation per second)
Clearly then, f = 1/T

25. Wave Speed
(v, c) This is the speed with which energy is carried
in the medium by the wave.
Measured in m s-1
A very important fact is that wave speed depends
only on the nature and properties of the medium

26. Eg
• For example, the speed of sound waves in air is
typically 330 ms-1
to 350 ms-1
depending on the
density of the air and is four times faster in water.
Velocity = displacement of crest/time taken
• If the time taken is equal to the period T of the
wave, the displacement of one crest in this time is
equal to λ and the equation can be rewritten as:
• v = λ/T
• But f = 1/T
• so v = fλ

27. Waves speed table
WAVE TYPE MEDIUM SPEED (ms-1
)
Sound Carbon Dioxide 260
Air 331
Hydrogen 1290
Pure Water 1410
Sea Water 1450
Glass 5500
Light Vacuum 2.997 x 108
Air 2.998 x 108
Glass (crown) 2.0 x 108
Earthquake Crust 3500 (transverse)
8000 (longitudinal)
Mantle 6500 (transverse)
11000 (longitudinal)

28. Eg 1
• What will be the time delay in hearing the
sound from a brass band for an observer
660 m away? Assume the light arrives
instantaneously and the sound travels at 330
ms-1
.

29. Solution
• v = 330 ms-1
• s = 660 m
• t = ?
• v = s/t
and rearranging;
• t = s/v
• t = 660/330
• t = 2.0 s

30. Eg 2
• Waves reaching the beach from an offshore
storm arrives at 4 s intervals. Calculate the
frequency of the waves

31. Solution
• T = 4 s
T = 1/f
• f = ¼
• f = 0.25 Hz

32. Eg 3
• Find the period of a 1 kHz sound wave.

33. Solution
• f = 1 kHz = 1000 Hz
• T = ?
• F = 1/T
• rearranging;
• T = 1/f
• T = 1/1000
• T = 0.001 or 10-3
s.

34. Eg 4
• Calculate the speed of an earthquake wave
with a wavelength of 2 km and a frequency
of 3 Hz.

35. Solution
∀λ = 2000m
• f = 3 Hz
• v = ?
• v = fλ
• v = 3 x 2000
• v = 6000 m s-1

36. Eg 5
• Given that the speed of sound in air is 330
ms-1
, find the wavelength of (a) 20Hz and (b)
20000 Hz sounds.

37. Solution
• Part (a)
• v = 330 m s-1
• f = 20 Hz
∀λ = ?
• v = fλ
∀λ = 330/20
∀λ = 16.5 m
Part (b)
v = 330 m s-1
f = 20 000 Hz
λ = ?
v = fλ
λ = 330/20 000
λ = 0.0165 m
λ = 1.65 x 10-2
m

38. A very important property associated with all waves
is their so-called periodicity.
Waves in fact are periodic both in time and space
and this sometimes makes it difficult to appreciate
what actually is going on in wave motion.
Periodicity

39. If we drew a diagram that froze time
on waves in water
We would have an instantaneous
snapshot of the whole of the water
surface
The next diagram shows the
periodicity of the wave in space

40. Displacement / Distance
displacement
distancep

41. The y-axis shows the displacement
of the water from its equilibrium
position
The graph is a displacement-
distance graph.

42. We now look at one part of the wave that is
labeled p and "unfreeze" time
The next diagram shows how the position of
p varies with time
This illustrates the periodicity of the wave in
time

43. Displacement / Time
displacement of point p from equilibrium position
time

44. The y-axis now shows the
displacement of the point p from
equilibrium
The graph is a displacement-time
graph.

45. The space diagram and the time
diagram are both identical in shape
If we mentally combine them we
have the whole wave moving both
in space and time.

46. And for Longitudinal Waves?
For the longitudinal wave in the
slinky spring the displacement-
distance graph actually shows the
displacement of the individual turns
of the spring from their equilibrium
position as a function of distance
along the spring.

47. However
It could equally show how the
density of turns of the spring varies
with length along the spring.

48. The displacement-time graph shows
the displacement of one turn of the
spring from its equilibrium positions
as a function of time.

49. Wavelength again!
Wavelength will therefore be equal
to the distance between successive
crests and successive troughs.

50. rarefactions
wavelength

51. Sound Waves
A longitudinal wave in a slinky
spring is analogous to a sound
wave in which each turn of the
spring represents an air molecule.

52. Interpreting Graphs - 1
displacement
distance
crest
trough
amplitude crest
wavelength
amplitude
wavelength

53. Interpreting Graphs - 2
displacement
time
amplitude
period
period

54. Deriving v = f λ
Imagine a wave with velocity v
Being produced from a source of
frequency f
In 1 second the 1st
wavefront would
have travelled a distance of f λ
As speed = distance / time
v = f λ / 1
∴ v = f λ

55. 2 Important Points
1. The frequency of a wave
depends only on the source
producing the wave
It will therefore not change if the wave
enters a different medium or the
properties of the medium change

56. 2. The Speed of waves only
depends on the nature and the
properties of the medium
Water waves do travel faster in deeper
water
Light travels slower in more optically
dense material

57. The EM Spectrum Itself
Short λLong λ
High fLow f
VISIBLERadio
Waves
Micro
Waves
Infra
red
Gamma
rays
Ultra
Violet
X
rays

58. Wavelengths of Regions (m)
• Gamma Rays <10-12
• X-rays 10-10
• Ultraviolet 10-8
• Violet 7.5 x 10-7
> Visible > Red 4.3 x 10-7
• Infrared 10-5
• Microwaves 10-2
• Radio and TV > 103

59. The Different Regions
In the context of wave motion, common
properties of all parts of the
electromagnetic spectrum are
all transverse waves
all travel at the speed of light in vacuo
(3.0 x 108
ms-1
)
all can travel in a vacuum

60. Sources of Regions
Gamma – certain radioactive material’s nuclei
X-rays – by firing an electron stream at a tungsten
metal target in a highly evacuated tube.
Ultraviolet – the Sun, ultraviolet lamp
Visible – hot bodies
Infrared – the Sun (heat), hot bodies
Microwaves – Ovens, communication systems
Radio and TV – transmitter stations, Azteca TV