Waves

A wave is a disturbance which travels through a medium and transfer energy from one point to another without causing any permanent displacement of the medium itself e.g. water waves, sound waves, waves formed when a string is plucked.
Many waves are invisible but have visible effects. In this chapter, you will study the properties and characteristics of waves and their effects on matter.

Types of waves:
We can classify all waves into two categories:
1. Mechanical waves
This is a type of waves produced by physical disturbance and requires a material medium for its
propagation. Examples of mechanical waves include water ripples, sound waves, waves on strings and
ultrasonic waves.
2. Electromagnetic waves
This type of waves does not require any medium for propagation and are caused by electrons
undergoing any energy change. Examples of electromagnetic waves include light waves, infra-red rays
and ultra-violet rays
Note: All waves are as a result of vibrations caused in the medium.

Wave motion

When a wave is set up on the medium, the particles of the medium vibrate from about a mean position as the wave passes. The vibrations are passed from one particle to the next until the final destination is reached.

Forms of waves

There basically two broad forms -:
a) progressive waves
b) stationary waves

Progressive waves

This is a wave which moves away from its source through a medium and spreads out continuously.
There are two kinds of progressive waves namely:
 Transverse waves
 Longitudinal waves

i. Transverse waves

These are waves in which particles vibrate perpendicular to the direction of propagation of the wave
e.g. water waves, light waves, waves formed when a rope is moved up and down.

ii. Longitudinal waves

These are waves in which the particles of the media vibrate in the same direction as the wave
OR
These are waves in which the particles of the media vibrate parallel to wave motion e.g. sound waves,
waves from a slinky spring.
Longitudinal waves travel by formation of compressions and rare factions. Regions where particles crowd together are called compressions and regions where particles are further apart are called rare factions.

General representation of a wave

Terms used in describing waves

1. Rest position (Mean position)
This is the line OQ where particles are stationary or displacement of a particle is zero (0)
2. Amplitude (a)
This is the maximum displacement of a particle from the rest position.
Displacement is the distance the object or particle is displaced from the undisturbed position or rest
position.
3. Cycle
This is one complete oscillation of the wave.
4. Wave length (λ)
 This is the distance between two successive crests or two successive troughs.
 This is the distance covered by one complete cycle of a wave.
 This is the distance between two particles of a wave vibrating in phase
 This is the distance between two successive compressions or rare factions.
5. Period
Is the time taken by a wave to perform one complete cycle, i.e. T= where n is number of cycles.
6. Frequency
This is the number of cycles a wave completes in one second i.e. F=
S.I. unit = Hertz (Hz)
8. Crest
It is the maximum displaced point above the line of 0 (zero) disturbance.
9. Trough
It is the maximum displaced point below line of zero disturbance.
Ray: A ray is a direction or a path taken by a wave. It is represented by a line with an arrow pointing
in the direction of the wave.

Phase: This is the state of vibration of a particle in a wave. Two particles are said to be vibrating in
phase if their state of vibration is the same.
Wavefront: This is a line or a section through an advancing wave in which all the
particles in that line are vibrating in the same phase
Example
Straight wavefronts

10. Wave velocity
It is the distance which the wave travels in one second in a given direction. S.I unit is m/s.

The wave equation
From the wave speed v = …..(i)
If the wave describes n cycles in time t
Then the distance covered d= nλ …. (ii)
Substituting for d in … (i) → v =
But f = hence v = fλ wave equation

Examples
1. A radio station produces waves of wave length 10m. If the wave speed is 3×108m/s, calculate
(i) Frequency of radio wave.
(ii) Period T
(iii) Number of cycles completed in 10s
(i) λ = 10m , v = 3×108m/s t = 10s
v = f λ → f = =

f = 3×107
(ii) Period T = = 3.3 × 10-8Hz
(iii) Number of cycles → f = → n = f t
= 3×107 × 10
= 3×108cycles

2. The distance between 10 consecutive crests is 36cm. Calculate the velocity of the wave if the
frequency of the wave is 12Hz.
Since;
d = (n – 1) λ
0.36 = (10 – 1) λ
0.36 = 9 λ
λ = = 0.04m
V= f λ
= 12×0.04
= 0.48m/s

(a) Name (i) Any two points on the wave which are in phase
(ii) Label M and x
(b) (i) Determine the amplitude of the wave.
(ii) If the speed of the wave is 80m/s, determine the frequency of the wave.
Questions
A vibrator produces waves which travel 35 m in 2 seconds. If the waves produced are 5cm from each
other, calculate;
(i) the wave velocity

(ii) wave frequency
(i) v = f λ → =
(ii)v = f→f =

Stationary waves
These are waves formed when two progressive waves of nearly the same amplitude and frequency moving in opposite directions meet e.g. when an incident wave meets its own reflection from a barrier. Stationary waves are formed in pipes and on stretched strings.

The distance between two neighbouring nodes is
Characteristics of stationary waves
 The stationary wave comprises of points where the displacement of particles is permanently
zero. They are called nodes (N).
 Between the nodes, particles are vibrating in phase, but they do not attain the same amplitude.
 Particles half-way between the nodes attain maximum amplitude. They are called antinodes (A).
(The broken lines show how the displacements of individual particles vary with time.)
 The peaks are always at the same position.

A ripple tank is an instrument used to study water wave properties. It is a shallow glass trough which
is transparent. The images of the wave are projected on the screen which is placed below it.
The waves are produced by means of a dipper which is either a strip of a metal or a sphere. When the
dipper is moved up and down by vibration of a small electric motor attached to it. The sphere produces
circular wave fronts and the metal strip is used to produce plane waves.
A stroboscope helps to make the waves appear stationery and therefore allows the wave to be studied
in detail.
N.B The speed of the wave in a ripple tank can be reduced by reducing the depth of water in the tank.
The effect of reducing speed of waves is that wave length of water reduces but frequency does not.
The frequency can only be changed by the source of wave.
WAVE PROPERTIES
The wave produced in a ripple tank can undergo.
(a) Refraction
(b) Reflection
(c) Diffraction
(d) Interference
REFLECTION OF WAVES
A wave is reflected when a barrier is placed in its path. The shape of the reflected wave depends on
the shape of the barrier.
The laws of reflection of waves are similar to the laws of reflection of light.
(i) Reflection by plane reflectors
(a) Reflection of straight wave front.

Note
During reflection of water waves, the frequency and velocity of the wave does not change.
REFRACTION OF WAVE
This is the change of in direction of wave travel as it moves from one medium to another of different depth. It causes change of wave length and velocity of the wave.

However, the frequency and the period are not affected. In a ripple tank, the change in direction is brought about by the change in water depth.

Refractive index,
DEFRACTION OF WAVES
This is the spreading of waves as they pass through holes, round corners or edges of obstacle. It takes
place when the diameter of the hole is in the order of wave length of the wave i.e. the smaller the gap
the greater the degree of diffraction as shown below.
(a) Wide gap

Sound waves are more diffracted than light waves because the wave length is greater than that of
light.
Therefore sound can be heard in hidden corners.
N.B – When waves undergo diffraction, wave length and velocity remain constant.

Interference of waves
This is the superposition of two identical waves travelling in the same direction to form a single wave with a larger amplitude or smaller amplitude. The two waves should be in phase (matching).

Constructive interference

This constructive interference occurs when a crest from one wave source meets a crest from another source or a trough from one source causing reinforcement of the wave i.e. increased disturbance is obtained. The resulting amplitude is the sum of the individual amplitudes.

Destructive interference
This occurs when the crest of one wave meets a trough of another wave resulting in wave cancelling
i.e.

Electro magnetic waves

This is a family of waves which is made by electric and magnetic vibrations of very high frequency. Electromagnetic waves do not need a material medium for transformation i.e. they can pass through a vacuum.

Spectrum of electro magnetic waves
In decreasing frequency

PROPERTIES OF ELECTROMAGNETIC WAVES
• They are transverse waves.
• They can travel through vacuum.
• They travel at a speed of light (3.0 ×108m/s).
• They can be reflected, refracted, diffracted and undergo interference.
• They possess energy.
EFFECTS OF ELECTROMAGNETIC WAVES ON MATTER
(a) Gamma rays.
• They destroy body tissues if exposed for a long time.
• They harden rubber solutions and lubricate oil to thickness.
(b) X- rays
• Causes barriers/curtains to give off electrons.
• Destroys body tissues if exposed for a long time.
• Used in industries to detect leakages in pipes and in hospitals to detect fractures of bones.
(c) Ultra violet
• Causes sun burn
• Causes metals to give off electrons by the process called photoelectric emission.
• Causes blindness.
(d) Visible light
• Enables us to see.
• Changes the apparent colour of an object.
• Makes objects appear bent to refraction.
(e) Infrared
• Causes the body temperature of an object to rise.
• It is a source of vitamin D.
(f) Radio waves
• Induces the voltage on a conductor and it enables its presence to be detected.

SOUNDS WAVES (LONGITUDINAL WAVES)
Is a form of energy which is produced by vibrating objects e.g. when a tuning fork is struck on a desk
and dipped in water, the water is splashed showing that the prongs are vibrating or when a guitar
string is struck.
SPECTRUM SOUND WAVES

SUBSONIC SOUND WAVES
These are not audible to human ear because of very low frequency of less than 20Hz
AUDIBLE SOUND WAVES
These are audible to human ear. This frequency ranges from
20Hz- 20 KHz.
ULTRASONIC SOUND WAVES
These are sound waves whose frequencies are above 20Hz. They are not audible to human ears.
They are audible to whales, Dolphins, bats etc.
APPLICATION OF ULTRASOUND WAVES
• They are used by bats to detect obstacles e.g. buildings a head.
• Used in spectacles of the blind to detect obstacles.
• Used in radiotherapy to detect cracks and faults on welded joints.
• Used in industries to detect rocks in seas using sonar.
• Used to measure the depth of seas and other bodies.
PROPERTIES OF SOUND WAVES
• Cannot travel in a vacuum because of lack of a material medium
• Can cause interference.
• Can be reflected, refracted, diffracted, planes polarized and undergo interference.
• Travels with a speed V = 330m/s in air.
TRANSMISSION OF SOUND
Sound requires a material medium for its transmission. It travels through liquid, solids and gases,
travels better in solids and does not travel through vacuum.
EXPERIMENT TO SHOW THAT SOUNDS CANNOT PASS THROUGH A VACCUM

 Arrange the apparatus as in the diagram with air in the jar.
 Switch on the electric bell, the hammer is seen striking the gong and sound is heard.
 Gently withdraw air from the jar by means of a vacuum pump to create a vacuum in the jar.
 The sound produced begins to fade until it is heard no more yet the hammer is seen striking the
gong.
 Gently allow air back into the jar, as the air returns, the sound is once again heard showing that
sound cannot travel through vacuum.
Note: The moon is sometimes referred to as a silent planet because no transmission of sound can
occur due to lack of air (material medium).
The speed of sound depends on;
(i) Temperature
Increase in temperature increases the speed of sound i.e. sound travels faster in hot air than
in cold air.
(ii) Wind
Speed of sound is increased if sound travels in the same direction as wind.
(iii) Density of medium.
Speed of sound is more in denser medium than in less dense. Change in pressure of air does
not affect speed of sound because density is not affected by change in pressure.
EXPERIMENT TO VERIFY THE LAWS OF REFLECTION OF SOUND

 Put a ticking clock in tube R on a table and make it to face a hard plane surface e.g. a wall.
 Put tube T near your ear and move it on either sides until the ticking sound of the clock is heard
loudly.
 Measure angle i and r which are the angles of incidence and reflection.
 From the experiment, sound is heard distinctly due to reflection.
 Angle of incidence (i) and angle of reflection (r) are equal and lie along XY in the same plane.
 This verifies the laws of reflection.
REFRACTION OF SOUND WAVES
Refraction occurs when speed of sound waves changes. The speed of sound in air is affected by
temperature. Sound waves are refracted when they are passed through areas of different temperature.
This explains why it is easy to hear sound waves from distant sources at night than during day.
REFRACTION OF SOUND DURING DAY

During day, the ground is hot and this makes the layers of air near the ground to be hot while that
above the ground is generally cool. The wave fronts from the source are refracted away from the
ground.
REFRACTION OF SOUND DURING NIGHT

During night, the ground is cool and this makers layers of air near the ground to be cool while above
to be warm. The wave fronts from the source are refracted towards the ground making it easier to
hear sound waves over long distances.
DEFRACTION OF SOUND
This refers to the spreading of sound waves around corners or in gaps when sound waves have wave
length similar to the size of the gap. It is due to refraction that a person behind the house can hear
sound from inside.
INTERFERENCE OF SOUND
When two sound waves from two different sources overlap, they produce regions of loud sound and
regions of quiet sound. The regions of loud sound are said to undergo constructive interference while
regions of quiet are said to undergo destructive interference.
EXPERIMENT TO SHOW INTERFERENCE OF SOUND

ECHOES
An echo is a reflected sound. Echoes are produced when sound moves to and fro from a reflecting
surface e.g. a cliff wall. The time taken before an echo arrives depends on the distance away from the
reflecting surface.
In order for a girl to hear the echo; sound travels a distance of 2d.
Velocity =
For an echo; velocity of sound,v =
Examples
1. A girl stands 34m away from a reflecting wall. She makes sound and hears an echo after 0.2
seconds. Find the velocity of sound.
v =
v =
= 340m/s
2. A person standing 99m from a tall building claps his hands and hears an echo after 0.6 seconds.
Calculate the velocity of sound in air.
v =
v =
= 330m/s
3. A gun was fired and an echo from a cliff was heard 8 seconds later. If the velocity of sound is
340m/s, how far was the gun from the cliff?
v =
340 =
1360 = d
d = 1360m
4. A student is standing between two walls. He hears the first echo after 2 seconds and then another
after a further 3 seconds. If the velocity of sound is 330m/s, find the distance between the walls.
V =
V =
Distance between the walls = d1 + d2

d1 =330m
d2 = 825m hence
Distance between the walls = d1 + d2 = 330+825 = 1155m
5. A man is standing midway between two cliffs. He claps his hands and hears an echo after 3 seconds.
Find the distance between the two cliffs.
(Velocity of sound = 330m/s)
V= 3 × 165 = 990m
d1
d1=495m
d1=d2
d1+d2 = 495+495
MEASUREMENT OF VELOCITY OF SOUND USING AN ECHO METHOD
Method;
A person stands a certain distance d from the reflecting surface (tall wall), then measure that distance.
Make a sharp clapping sound by banging two blocks of wood together.
Repeat the sound at regular time intervals to coincide exactly with the echo.
Count the number of claps in a given time t
Find the time taken for one clap i.e.
Velocity =
Velocity =
Velocity =
Example
A student made 50 claps in one minute. If the velocity of sound is 330s, find the distance between the
student and the wall.
Velocity =
d=198m
REVERBERATION

In a large hall where there are many reflecting walls, multiple reflections occur and cause or create an
impression that sound lasts for a longer time such that when somebody makes a sound; it appears as
if it is prolonged. This is called reverberation.
Definition of Reverberation
Reverberation is the effect of the original sound being prolonged due to multiple reflections.
ADVANTAGES OF REVERBERATION
In grammar, reverberation is used in producing sound. Complete absence of reverberation makes
speeches inaudible.
DISADVANTAGES OF REVERNERATION
During speeches, there is a nuisance because the sound becomes unclear.
PREVENTION OF REVERBERATION
The internal surfaces of a hall should be covered with a sound absorbing material called acoustic
material.
WHY ECHOES ARE NOT HEARD IN SMALL ROOMS?
This is because the distance between the source and reflected sound is so small such that the incident
sound mixes up with the reflected sound making it harder for the ear to differentiate between the two.
Question
1. Outline four properties of electromagnetic waves.
2. Distinguish between
i. sound waves and light waves.
ii. sound waves and water waves
3. A man standing midway between two cliffs makes a sound. He hears the first echo after 3s.
Calculate ‘the distance between the two cliffs (Velocity of sound in air = 330m/s)
Musical notes
Music
This is an organized sound produced by regular vibrations.
Noise
This is a disorganized sound produced by irregular vibrations.
Musical note
This is a single sound of a certain pitch made by a musical instrument or voice.
Characteristics of musical notes
Pitch

This is the loudness or softness of sound. It depends on the frequency of sound produced, the higher
the frequency the higher the pitch.
Timber
This is the quality of sound produced, it depends on the number of overtones produced, the more the
number of overtones, the richer and the sweeter the music and therefore the better the quality.
Overtone
This is a sound whose frequency is a multiple of a fundamental frequency of the musical note.
Beat
This refers to the periodic rise and fall in the amplitude of the resultant note.
Loudness
This depends on the amplitude of sound waves and sensitivity of the ear.
Amplitude
This is the measure of energy transmitted by the wave. The bigger the amplitude, the more energy
transmitted by the wave and the louder sounder sound produced.
Sensitivity of the ear
If the ear is sensitive, then soft sound will be loud enough to be detected and yet it will not be detected
by the ear which is insensitive.
Pure and impure musical notes.
Pure refers to a note without overtones. It is very boring and only produced by a tuning fork.
Impure refers to a note with overtones. It is sweet to the ear and produced by all musical instruments.
VIBRATION IN STRINGS
Many musical instruments use stretched strings to produce sound. A string can be made to vibrate by
plucking it like in a guitar or in a harp in pianos. Different instruments produce sounds of different
qualities even if they are of the same note.
Factors affecting the frequency of the stretched string
(a) Length
For a given tension of the string, the length of the string is inversely proportion to the frequency of
sound produced. This can be demonstrated by an instrument called sonometer as shown below.

A- Fixed bridge
B- Movable bridge
C- Wheel
D- Stretched string
R-Load
By moving bridge B, higher frequency can be obtained for a short length AB and lower frequency for a
long length AC. The relation can be expressed as f
(b) Tension
Adding weights or removing them from its ends at load R varies the tension of the sonometer wire. It
will be noted that the higher the tension, the higher the frequency of the note produced.
(c) Mass per unit length (m)
Keeping length (l) and tension (t) constant, the frequency of sound produced depends on the mass per
unit length of the string. Heavy strings produce low frequency sounds. This is seen in instruments such
as guitar, base strings are thicker than solo stings. If the tension and length are kept constant, the
frequency of sound is inversely proportional to the mass per unit length of the strings thus a thin short
and taut string produces high frequency sound. (f )