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6.7 Sound Wave

Producing sounds

Sound waves are longitudinal waves that are transmitted through almost any substance i.e  solid , liquid or gas.


The waves are produced by any mechanism which produces compression  vibrations of the surrounding medium. Some examples are the vibrating string of a guitar, exploding gas in firecracker  and the vibrating diaphragm of a loudspeaker.


Vibrations in a vacuum

Sound cannot travel through a vacuum because in a vacuum there is no material to transmit the compressions. A common demonstration of this to show  that is a ringing bell cannot be heard if the bell is in a vacuum chamber. The bell is vibrating , but there is no surrounding material to carry the vibration to our ears.

Similarly we cannot hear the nuclear explosions on the sun because there is no medium in space. Astronauts cannot speak to each other on the moon  without using radio waves, because  there is no air on the moon through which sound waves can travel.


Sound waves in air


Sound waves are longitudinal waves. The sound waves from a loudspeaker produce compressions and rarefactions of the air molecules. When molecules pushed forwards (to the right) meet molecules bouncing backwards(to the left) , after collisions with other molecules in front, a region of compression is produced where the air pressure is higher. In between the compressions are rarefactions where the number of molecules is reduced and air pressure is lower.

Thus  we may describe  a progressive wave sound in air as a travelling pressure wave in which regions of increased air pressure travel along where the air molecules are compressed together separated by regions of reduced air pressure at the rarefactions.

Speed of sound

Sounds travels quickly, but not nearly as fast as light. The speed of sound waves depends on the medium. Sound travels fastest in solids, and slowest in gases.

Sound travels more quickly through medium in which the atoms are strongly bound together. If you imagine that in a solid  all the atoms are joined together by springs then the stronger the springs the faster the sound travels. The strong binding between atoms in solids means that sound will travel much more quickly through solids than through gases.

The speed of sound waves in gases  increase when the density  of  the gases decrease. When the density of the gases decrease ,the frequency of the vibrations increase ,so the  speed of the sounds increase ( v = fλ)

The speed of the sound waves also increase as the temperature the gases increase. It is because when the temperature of the gases increase the density of the gases decrease.

The speed of sound waves in a gas not affected by changes of pressure.

Typical values for speed of sound are given in the following table.


Speed of sound waves/ ms-1

Air (0oC)


Oxygen (0oC)


Helium (0oC)


Hydrogen (0oC)


Water (0oC)


Water (20oC)


Water (50oC)


Aluminium (0oC)


Copper (0oC)


Iron (0oC)


The frequency spectrum of sound waves


If a signal generator is connected to a loudspeaker , not all the frequencies of the sound wave is produced ca be heard by the human hear.

The human hear is capable of hearing sounds with frequencies in the range of 20 Hz to 20 000 Hz.

The following figure shows the frequency spectrum of sound waves:


Below about 20 Hz the vibrations are felt rather than heard e.g. earth quakes and are called subsonic.

We are able to hear sounds with frequencies from around 20 Hz to almost 20 000Hz.

Sounds above the upper hearing limit are called ultrasound.

Dogs, bats and dolphins are all known to be able to hear sounds whose frequency is well above the limits of human hearing.


Loudness and Pitch of sound


The loudness of  a sound depends on the amplitude of vibrations. As the amplitude of vibrations increase, the loudness of  a sound increases.


The pitch of  a sound depends on the frequency of vibrations. As the frequency of vibrations increase , the pitch of  a sound increases.


Quality or timbre of sound

The quality of sound depends on the wave form.

Different musical instruments of the same pitch are distinguished from each other by their quality.


Sound and Noise

Our ear can also tell the difference between musical sounds and noises. The waveforms produced by musical instruments are regular, whilst those produced by noises are jagged  and irregular.


Application of Sound Waves


(1)     Ultrasonic scanning in medicine involves sending ultrasound waves into the patient’s body and detecting the echoes which come back. This can be used , for example, to see the position of an unborn baby inside its mother’s womb. The whole process is completely painless and much safer than using X-rays.

(2)     Sound waves of high energy are directed to the kidney stones to destroy them in the cavity of the kidney. The disintegrated particles are removed during urination by the patient.

(3)     Dentist  use ultrasonic waves to remove plaque from the teeth.

(4)     Ultrasound spectacles help blind persons to estimate the distance away of something in front of them.


(1)     Ultrasonic scanning is used to detect cracks in metal structures .  This is how aircrafts parts are checked for hidden cracks which might prove dangerous later.

(2)     A goldsmith uses high frequency sound waves to dislodge dirt particles adhering to jewellery and precious stones.

(3)     Ships use echo-sounding equipment to find how deep the water is. The time interval is measured between a pulse of sound and its echo from the sea bed.

          If the echo-sounders measures an interval of time ,t  , and the speed of sound wave in water is v, the depth , d can be calculated as follows;


          Distanced travelled  by pulsed = speed x time

                                                             2d= v x t

so the  distance d:



(4)       In modern fishing trawlers, echo -sounding 

Produces SONAR ( Sound Navigation and Ranging) is used to detect shoals of fish. The equipment can detect the reflected pulse from the shoal, and work out its position and depth

(5)       Geologists also use echo – sounding methods to locate boundaries between rock layers far below the surface. This is useful, for example in finding places where it might worth drilling for oil. A small explosion on the surface sends a sound wave downwards into the Earth , and some of the sound is reflected from the boundaries between rock layers. The detector measures the time interval between the sound and the echoes. From this, the depth of the rock layers can be measured.


Example 1


A Sonar signal sent vertically  downwards from a ship is reflected  from the ocean floor and detected by  a microphone on the keel  0.8 s after transmission . If speed of sound in water is 1 500 ms-1, what is the depth of the ocean?








Example 2


A man stands in front of a fairly large flat wall at a distance 50 m.  He claps his hands and the time for 20 intervals between claps is 12 s. What is the speed of the sound ?



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