This unit is about Echoes as studied in physics.


An echo is a sound reflected from a hard surface. For an echo to be heard distinctly from the original sound, it must arrive at least o.1s later.

Since speed of sound in air = 330ms-1

Distance travelled by sound

= speed x time

= 330 x 0.1

= 33m

Hence the minimum distance of wall from the listener

= 33/2

= 16.5

= 17m


Reverberation is the effect in which the original sound appears to be prolonged due to the echo mixing up with the original sound. This occurs when the reflecting surface is at a distance less that 17m from the observer/ source.

Reverberation improves audibility but excessive reverberation makes sound indistinct or confused

To measure the velocity of sound by the echo method

The experiment requires two people, one to make the sound and the other to carry out the timing. The first person claps two wooden blocks and listens for the echo from the wall. He / she adjusts the rate of striking such that each clap coincides with the echo of the previous clap.

The time interval between two successive claps in equal to the time taken for sound to travel twice the distance between the observers and the wall. The second observer starts the clock and records time for the successive clap intervals. The distance of one clapping from the wall is measured and recorded

Suppose that the distance is x meters

Then sound travels a distance 2x in time t/n


The experiment is repeated and the average value of the velocity of sound is calculated.


Echo sounding

Ships always carry a special sound transmitter an echo sounder called fathometer for measuring the depth of the sea. The fathometer sends out regular sound impulses which are reflected back from the sea bed and received by the receiver called a hydro phone.


If the velocity of sound is known, the depth of the sea at any point cone is determined by measuring the time it takes for sound to travel to and fro.


Echo sounding offers security to the ships especially in uncharted water where solid objects are likely to be encountered. These many include submarines, ice cargo or a sunken ship. Sound wave sent out by the ship has a very high frequency and cannot be detected by the human ear. Ultrasonic waves re waves of very high frequency

Application of ultrasound

  1. Used to monitor the development of an unborn baby in hospitals
  2. Bats use ultrasound for navigation
  3. Used in medical and surgical diagnosis to examine tissue e.g. muscles and bones


An echo sounder of a ship received the reflected waves from a sea bed after 0.2 seconds. What is the depth of the sea bed if the velocity of sound in water is 1450ms-1?

Time taken to reach seal bed = 0.2/2

= 0.15

Distance = speed x time

= 1450 x 0.1

= 145m

Hence depth of seabed is 145m

Refraction of sound

Sound can also be refracted. Refraction takes place at the boundary of two media, just like light, for which the refractive index is different.

Speed of sound changes at a boundary. In open air, refraction occurs as sound travels from one layer of air to another. The temperature of various layers decrease with altitude.


When two notes of equal frequency with the same amplitudes are sounded together, the loudness increases and decreases periodically. These alterations in loudness are called beats.

The number of beats per second given by two notes of nearly equal frequencies F1 and F2 is given by F2 – F1. Beats are used to tune musical instruments.

Musical sounds

A musical note is educed by vibrations that are regular and repeating i.e. periodic motion. A sound of regular frequency is called a musical note/ tone and music is a combination of such tones.

Noise is a sound of irregular frequency that is not pleasing to the ear.


Characteristics of a musical note

  1. Loudness

This depends on the listener. Loudness of sound depends on the intensity of the sound. Intensity of sound is defined as the rate of flow of energy per unit area perpendicular to the directions by a point source, intensity at a distance r from the source is


Intensity of a sound is also proportional to the square of amplitude of vibration of the air.

  1. Pitch

This depends on the frequency of vibration of its source. A high frequency produce a high pitched note while a low frequency produce a low pitched note

  1. Quality

The same note played on two different instruments does not sound the same. The notes are said to have different quality


A stationary wave is one that is formed when two progressive waves with the same amplitude and frequency travelling in opposite directions superpose.

If a string is connected to a vibrating fork to one end and is kept taut by weights on the other end, a progressive wave is formed.

When the string vibrates, the wave is reflected at the other end. A stationary wave is created.


These are points where the displacement of the vibrating particles is always zero.

Antinodes, these are points between nodes of maximum amplitude of vibration.


A progressive wave is one in which there is energy transfer from one point to another due to a disturbance of the source of the wave.

Stringed instruments

These include violins, guitars and harps among others. The strings vary in length and thickness harp and guitar strings are caused to vibrate by plucking them, while the piano strings are struck by feet hammers.

A violin has only four strings of different thickness but the same length


A string is a tightly stretched wire fixed at both ends.

Experiment to show how frequency of a vibrating string depends on the length of the string


A sonometer is used. It consists of a hollow box Q with a thin horizontal wire fixed at one end A and passing over a grooved wheel at the other end with a mass suspended to keep it taut. Wooden bridges B and C are placed beneath the wire to obtain a definite length.

The length L of the wire between B and C varied by moving C until the note obtained by plucking BC in the middle is the same as that produced by a sounding turning fork of frequency F.

The experiment is repeated with increasing values of F obtained from other turning forks and the corresponding length of L of the wire between B and C is measured. A graph of F against I/L    is plotted and is found to be a straight line graph through the origin.

Thus F= I/L    for a given tension. Frequency is inversely proportional the length of the strings


The mass suspended on the wire should be kept constant

Other factors that affect the frequency of a vibrating string

  1. Tension

From the experiment, frequency is proportional to the square root of the tension-T – F

  1. Mass per unit length

The thicker the string, the lower the frequency for a given length and tension. From experiment,




Fundamental frequency

This is the lowest frequency produced by a musical instrument. It is also called the first harmonic. An overtone is a note that is a multiple of the fundamental frequency. Overtones with frequencies 2f, 3f, 4f are the second, third and fourth harmonic respectively. For a closed pipe, the first overtone is the third harmonic

Damped oscillations

The amplitudes of the oscillation of a simple pendulum gradually decrease to zero with time due to resistance from the air. Such a motion is said to be damped. Un damped oscillations are said to be free. There is no air resistance to their motion and their amplitude of vibration remains constant.

If a system is slightly damped, oscillations of decreasing amplitudes occur. Where heavily damped, no oscillation occurs and the system returns very slowly to its equilibrium position. When the time taken for the displacement to become zero is minimum, the system is said to be critically damped.




Resonance is said to occur when a system is set in oscillation at its natural frequency as a result of impulse received from another system which is vibrating with the same frequency.

Application of resonance

  1. In tuning a radio set
  2. Turning a son meter wire
  3. Diving on a spring board.

Resonance in a tube or a pipe

If one blows through a closed pipe the air inside vibrates and slowly note is obtained from the pipe which is its fundamental.

When a fork of the same frequency as the fundamental is held over the pipe, the air inside is set in resonance by periodic force the amplitude of vibration is large.

A laud note with the same frequency as the fork is heard coming from the pipe and a stationary wave is set up. The top of the pipe acts as antinodes and the fixed as the node.


If the sounding turning fork is held over a pipe open at both ends, resonance occurs when the stationary wave in the pipe has antinodes at the two open ends.

Measurement of velocity of sound in air using a resonance tube

A glass tube which can be drained from the bottom is filled with water. A sounding turning fork of frequency F is brought to the mouth of the tube. The water is slowly drained until a laud sound is heard.

The tap is closed and the length L of the air column is measured.


The turning fork is again sounding at the mouth of the tube and the water drained further until a loud sound is heard again.

The top is closed and the length L2 of the column is measured. The velocity of the sound in air is then calculated from,-

V = 2f [L2 – L1]

Vibrations in a closed pipe or tube


A stationary wave is set up with the open end being an antitrade [A] and the closed end a node [N]


This is the frequency of the lowest note obtained from the pipe and it is called the fundamental. Overtones of a closed pipe have frequencies 3f, 5f, and 7f.

Vibrations in an open pipe



When air is blown into an open pipe, a stationary wave is setup as shown above. Both ends are antinodes.


This is the frequency of the fundamental note of the pipe. The frequencies of the overtones in the open pipe are 2f, 3f, 4f….

Difference between progressive and stationery waves

Progressive waves Stationary waves
There is energy flow along the wave There is no energy flow
Vibrations are of the same amplitude and frequency  Amplitudes are different and depend on position along the wave
Particles in phase are n λ distance Particles in phase are n  distance
Apart where n = 1, 2, 3………………. Apart where n = 1, 2, 3……………..


Difference between sound and light waves

Sound waves Light waves
Do not travel through a vacuum Can travel through a vacuum
Are longitudinal waves Are transverse waves
Cannot be polarized Can be polarized



ASSIGNMENT : ECHOES assignment MARKS : 10  DURATION : 1 week, 3 days

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