There are two types of waves
and pulses that we encounter
in the physical world.
In these waves the source that produces the wave
oscillates at right angles to the direction of travel of
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.
Direction of travel
of the wave
Direction of oscillation
of the particles
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.
Direction of travel
of the wave
Direction of oscillations
of the particles
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
• List 6 types of wave and classify them
according to the types you have just learnt.
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.
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.
The substance or object in which the wave is
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.
Water waves however, can be a bit
Waves at sea do not transport water but the
Similarly, a wave on a lake does not transport
water but water can actually be blown along
by the wind.
(s) is the distance that any particle
is away from its equilibrium position
at an instance
Measured in metres
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
A term coined from water waves
referring to the points at the lowest
part of the wave.
The negative displacement from
This is a term used in connection with
longitudinal wave and refers to the region
where the particles of the medium are
A term used in connection with longitudinal
waves referring to the regions where the
particles are "stretched out".
() 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
(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
Normally measured in metres
(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
(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
(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
• 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 and the equation can be rewritten as:
• v = /T
• But f = 1/T
• so v = f
Waves speed table
WAVE TYPE MEDIUM SPEED (ms-1)
Sound Carbon Dioxide 260
Pure Water 1410
Sea Water 1450
Light Vacuum 2.997 x 108
Air 2.998 x 108
Glass (crown) 2.0 x 108
Earthquake Crust 3500 (transverse)
Mantle 6500 (transverse)
• 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
• v = 330 ms-1
• s = 660 m
• t = ?
• v = s/t
• t = s/v
• t = 660/330
• t = 2.0 s
• Waves reaching the beach from an offshore
storm arrives at 4 s intervals. Calculate the
frequency of the waves
• T = 4 s
T = 1/f
• f = ¼
• f = 0.25 Hz
• f = 1 kHz = 1000 Hz
• T = ?
• F = 1/T
• T = 1/f
• T = 1/1000
• T = 0.001 or 10-3 s.
• Calculate the speed of an earthquake wave
with a wavelength of 2 km and a frequency of
• = 2000m
• f = 3 Hz
• v = ?
• v = f
• v = 3 x 2000
• v = 6000 m s-1
• Given that the speed of sound in air is 330
ms-1, find the wavelength of (a) 20Hz and (b)
20000 Hz sounds.
• Part (a)
• v = 330 m s-1
• f = 20 Hz
• = ?
• v = f
• = 330/20
• = 16.5 m
v = 330 m s-1
f = 20 000 Hz
v = f
= 330/20 000
= 0.0165 m
= 1.65 x 10-2 m
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.
If we drew a diagram that froze time
on waves in water
We would have an instantaneous
snapshot of the whole of the water
The next diagram shows the
periodicity of the wave in space
The y-axis shows the displacement
of the water from its equilibrium
The graph is a displacement-
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
Displacement / Time
displacement of point p from equilibrium position
The y-axis now shows the
displacement of the point p from
The graph is a displacement-time
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.
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.
It could equally show how the
density of turns of the spring varies
with length along the spring.
The displacement-time graph
shows the displacement of one turn
of the spring from its equilibrium
positions as a function of time.
Wavelength will therefore be equal
to the distance between successive
crests and successive troughs.
Interpreting Graphs - 2
Deriving v = f
Imagine a wave with velocity v
Being produced from a source of
In 1 second the 1st wavefront would
have travelled a distance of f
As speed = distance / time
v = f / 1
v = f
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
2. The Speed of waves only
depends on the nature and the
properties of the medium
Water waves do travel faster in deeper
Light travels slower in more optically
The EM Spectrum Itself
High fLow f
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
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
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