BS Physics (Foundation) Series

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Module # 46
Sound Waves & Acoustics
Sound
It is the branch of physics that deals with the origin, propagation
and reception of vibrations.
Sound is always produced from somebody which is vibrating.
These vibrations produce compressional waves in air surrounding
the body. These compressional waves also called sound waves
traveling through the air reach the receiver (the ear of the listener)
and produce sensation of sound.
Sound is a form of energy which is produced due to the vibrations
of a certain body.
So, we can say that a body produces sound when it vibrates. We
can see or feel the vibrations or disturbances in a body when
sound is produced in it.
Three things are necessary to produce sound.
(i) Vibrating body
(ii) Medium, and
(iii) Receiver like ear.

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Examples
1. We can produce sound in a metallic utensil by hitting it with
a spoon. If we touch the utensil with our hand gently, we will feel
vibrations in it.
2. Sound can be produced by hitting a tuning fork on a rubber
pad. To see the vibrations (sound) produced in it; bring a pith ball
suspended by a thread near one of the prongs. The pith ball will
fly away as soon as it touches the vibrating prong.
3. If we switch on a radio and make its sound louder, its
cabinet will start vibrating. If we place some pieces of paper on its
cabinet, then, they will also start vibrating.
From the above discussion and examples, we conclude that
"Sound is produced only if a body is vibrating".
Propagation of Sound
When sound is produced, it reaches the ear of a listener through
a medium. Without any medium, sound does not reach our ear.
The most important medium for sound is air. Whenever, a body is
vibrating, it produces a disturbance in the surrounding air. This
disturbance reaches our ear in the form of waves, thus, producing
the sensation of sound.

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Experiment
Suspend an electric bell in a bell jar by passing its wires through a
cork fixed in the mouth of the bell jar. Ring the bell and we will
hear the sound of bell clearly. Now, produce vacuum in the bell jar
with the help of the exhaust pump. Again, ring the bell. At this
time, sound will not be heard although the hammer is still seen
striking the bell.
From this experiment, it is clear that sound travels from one place
to another through a medium.
Velocity of Sound
Experiment
Select two stations at a distance of 8 km to 10 km such that there
is no obstacle between them. Fire a gun at a station A and ask
your friend at station B to start a stop watch on seeing the flash.
The stop watch should be stopped on hearing the sound of the
fire of the cannon. In this way, the time "t" taken by the sound to
travel from station A to station B is measured. The distance
between the two stations is already known. So, the velocity of
sound can be measured as:

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Fig: Speed of sound is measured by dividing the distance covered
by sound with time taken.
S = V x t
OR
V = S/t
Source of Error
If the direction of sound is opposite to that of air, then, the
apparent velocity of sound will be slightly less than the actual
velocity. But, in case of same direction, the velocity of sound will
be slightly greater than the actual velocity. This error can be
removed by measuring the time interval t1 between the sound of
gun firing at station A and the flash seeing at station B and then
by measuring the time interval t2 between the sound of gun firing
at station B and the flash seeing at station A.
The average time is calculated as follows:
Distance between two stations = s
t1 + t2
Average Time = t = -----------
2

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Distance s
Velocity of Sound = v = ---------------------- = -----------
Average time t
Velocity of sound is different in different media. In air, at O°C, the
velocity of sound is 330 m/s while in water it is 1450 m/s, and in
iron, the velocity of sound is 5130 m/s.
Velocity of Sound Waves
The velocity of sound waves in air is about 1130 ft/sec.
Sound Recording
All sounds produce vibrations in a material medium. If these
vibrations are recorded on some sort of disc or tape, then, we can
reproduce, at any time, the original sound from the impressions
made on the disc or tape during the recording process. In the
past, gramophone records or discs were very popular for listening
to recorded music. The technique of preparing commercial
records or discs is as follows.
Sound is converted into fluctuating electric current by a
microphone. This current is then amplified and actuates an
electromagnetic head with an attached cutting tool. The cutting
tool cuts a wavy groove running from the edge to the centre on a
metallic plate.

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Fig: A Gramophone Record
Sound is reproduced from the record by placing it on the turntable
of a gramophone. The turntable revolves with a fixed speed and a
fine needle set in a pickup arm is forced to move to and fro
laterally by the wavy groove. The vibrations of the needle are
converted into a fluctuating electric current, which is amplified and
then sent to a loud speaker. The recorded sound is thus
reproduced.
The technique of sound recording used in later/next tape
recorders is much easier than that of gramophone. In a tape
recorder, when someone speaks in front of a microphone, sound
is converted into fluctuating electric current. This current after
amplification actuates an electromagnetic recording head.
Meanwhile, a plastic tape coated with a magnetizable material
ferric oxide or chromium oxide is passed in front of the recording
head. A continuously varying magnetic field produced by the

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recording head magnetizes different parts of the moving tape with
varying intensity. Sound is thus recorded on the tape in the form
of magnetic patterns. To reproduce sound, the recorded tape is
passed in front of the play back head which gives rise to (in
proportion to the magnetism on different parts of the tape) a
fluctuating electric current. This fluctuating current is amplified
and then passed on to a loud speaker. This is, how sound is
produced from the recorded tape. In contrast with the
gramophone records, the sound recorded on the tape can be
wiped out by demagnetization and the same tape can be used
over and over again.
The sound track which accompanies a motion picture is
sometimes recorded by electromechanical devices as a small
variable density sound track on the edge of the film. The sound
waves are converted into a small transparent strip on the side of
the film with variations in the film density corresponding to the
variations in the voice current. Light that is allowed to shine
through the sound track will then have variations corresponding to
the voice or music recorded on the film. These variations in light
energy are converted into corresponding changes in electric
energy by a photo-electric cell. These are amplified and then
converted into sound by loud-speakers.

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Quality or Timber of Sound
The characteristic of sound by which we can distinguish between
two sounds of same pitch and loudness is called quality or timber
of the sound. Mostly, it is applicable to the musical instruments.
The sounds of flute and violin of same pitch and loudness are
easily recognized due to this characteristic.
Audible Frequency Range or Frequency Response of Ear
An average human ear can hear a sound if its frequency lies
between certain limits. If the frequency of a sound is higher than
20,000 hertz, then, it cannot be heard by the human ear. Sounds
of frequency higher than this range are called ultrasonic meaning
beyond or above sound. The sensitiveness of ear for higher
frequency sounds decreases with age. Children can generally
hear sounds of 20,000 hertz frequency, while, elderly people
cannot hear anything above 15,000 hertz. Moreover, we are not
able to hear sound below a certain frequency about 20 hertz.
These do not blend into a note, but, are heard separately.
The individual sensitivity of an average human ear is different in
different frequency ranges even if the frequency lies within the
lower and the upper limit of frequency.

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20 100 1000 10000 20000
Frequency
Range of Audible Frequencies
The body producing sound is always vibrating. But the sound of
every vibrating body is not heard. It is so because a human ear
can hear only those sounds which have the frequency between
20Hz to 20 000 Hz. This is called audible range of sound. An ear
can neither hear a sound of frequency less than 20Hz nor the
sound having a frequency more than 20,000 Hz. Different persons
have different audible range. This range varies with the age, e.g.
a child can hear sound of 20,000 Hz while an old man can hear
sound of 10,000 Hz to 15000 Hz.
Radio Frequency Range
The range of radio frequency lies from 535 KHz to 1705 KHz for
AM radio band and lies in between 88 MHz to 108 MHz for FM
radio band.

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Audio Frequency Range
The audio range consists of frequencies that can be heard in the
form of sound waves by the human ear.
Ultrasonics
Sound wave of frequency more than 20,000 Hz is known as
ultrasonic.
Ultrasonic waves are longitudinal waves with frequencies above
the audible range. This type waves are usually produced by
setting a quartz crystal to oscillate electrically. This device can
produce ultrasonic waves of the order of 109
Hz or more.
Ultrasonic waves are used as diagnostic, therapeutic and surgical
tools in medicine and in industrial applications.
Uses
(1) To determine the sea depth
Ultrasonic waves can be used in echo depth sounding devices to
determine the depth of the sea floor. Since, the wavelengths of
ultrasonic waves are much shorter than those of normal sound
waves, so, they can penetrate deep into the sea.
(2) Sonar

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Radar cannot be used under the sea as sea water absorbs
microwaves. Sonar is, therefore, used because it emits ultrasonic
waves and can be used to find out the location of an object by its
echo.
(3) Use as a detector
Since ultrasonic waves are used to find out the location of an
object by its echo, therefore, this principle is used to make
ultrasonic guidance devices for the blinds to detect cracks in
metal structures, to kill bacteria and micro-organism in liquids.
Ultrasonics are used to obtain cross sectional pictures of patients
in hospitals.
(4) Use in medicine
Ultrasound scans are usually preferred to x-rays scans because
ultrasound is much safer than x-ray. Ultrasound and x-rays are
used for different purposes in medicine. Ultrasound is considered
best to examine the fleshy parts of the body, whereas, x-rays are
better for examining suspected bones which are denser than
flesh.
Ultrasonic scanning helps the surgeons to picture the interior of
delicate parts of human or animal body such as eyes, kidneys and
wombs.

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(5) For cleaning purpose
Ultrasound is also used for cleaning places and objects which
cannot be cleaned in a normal way. Ultrasound cleaners are used
by jewelers and material scientists for cleaning delicate
instruments and materials.
Ultrasonic Frequencies Range
The range of ultrasonic frequencies lies from 16,000 Hz up to
several megahertz.
Sonic Frequencies
Frequencies below 16,000 Hz are called sonic or sound
frequencies.
Interference of Sound Waves
When two sound waves of the same frequency, wavelength and
amplitude superimpose on each other, then, they cancel each
other at some points and reinforce at other points. This
phenomenon is known as interference.
Experiment to Demonstrate Interference of Sound
The apparatus consists of a tube having two branches; the length
of one branch ACB is constant whereas that of the other branch

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ADB can be changed. The part D can slide over the part C as
shown in the figure below:
Fig: The sound waves from a tuning fork reach the ear at point B
through two paths.
The ear hears either a loud or a weak sound, depending upon the
lengths of the paths travelled by the two parts.
A vibrating tuning fork of high frequency is held horizontally in
front of the opening A. The sound waves on entering A will split;
half of the intensity goes through the tube C and the remaining
half goes through the tube D. The two parts re-unite at the outlet
B and can be heard by the ear held close to the point B.
The length of the sliding tube D is adjusted in such a way that the
path ACB is equal to the path ADB. Therefore, the path difference
is zero and, thus, constructive interference will take place and a
loud sound will be produced and heard at point B. If, on the other
hand, the sliding tube D is drawn out, then, the path ADB

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becomes longer than the path ACB. The sound waves arriving at
B via D will fall more and more behind those coming via C. When
the difference of path between the two waves is half a
wavelength, then, the sound produced is very faint due to
destructive interference. If the rubber portion of the tube C is
pinched (or pressed) so as to stop the sound waves coming
through C, then, the ear will again hear the sound due to waves
coming through ADB. This shows that the silence is due to the
destructive interference of two sound waves.
Silence Zones
Consider a high power fog-siren S situated on a high cliff to warn
an approaching ship. When the ship approaches the cliff, then, a
place comes where the sound of the fog-siren is not heard. This
place is called the silence-zone. When the ship moves towards or
away from the cliff, then, it comes out of the silence zone and the
sound is heard again. This zone of silence is due to destructive
interference as explained below:

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Fig: The sound of the siren is not heard at L when the waves
interfere destructively.
The sound of the siren S reaches the listener L on the ship
through two paths, one by the direct path SL and the other by the
path SCL after suffering reflection from the surface of the sea.
For SCL-SL = n, where, n = 0, 1, 2, 3, ----------, etc.
Constructive interference takes place and resultantly a loud sound
is heard.
While, for SCL-SL = (2n + 1) /2, where, n = 0, 1, 2, 3..... etc.
Destructive interference takes place and no sound is heard.
Acoustics
Application of the results of scientific study of sound in the design
of buildings, halls, concert rooms, etc. is called acoustics which is
concerned with the production, properties and propagation of
sound waves.

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In an acoustically well-designed hall, speech or music is distinctly
audible at all its places.
In most of the halls, this quality is generally lacking. One may
hear loud sound at some spots and very feeble at others. These
spots are respectively known as loud spots and dead spots.
The factors that adversely affect the acoustics of these halls are
(1) Resounding or echoes,
(2) Reverberations, and
(3) Focusing of sound at certain spots.
Echoes are produced by the reflection of sound from a large, flat,
hard surface such as a wall or a cliff. The time which elapses
before the reflected sound arrives as an echo, depends on the
distance of the reflecting surface from the source producing
sound. It has been seen that a normal human ear can hear two
sharp sounds separately (or distinctly) if the time interval between
them is at least 0.1 second. Therefore, for an echo to be heard
distinctly from the original sound, the echo must arrive at least 0.1
second later. If some sound enters the ear within this interval of
time, then, it merges with the previous sound and does not
appear to be separate (or distinct). To hear an echo, it is,
therefore, necessary that the time elapsed between the

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production of a sound and the hearing of its echo is equal to or
more than 1/10th of a second.
As the speed of sound is about 330 ms-1
, so, the sound wave
must travel a distance of 330 x 0.1 = 33m (S = vt) and
consequently the minimum distance of the wall must be about 17
m in order to give rise to an echo.
The formation of echoes in public halls which are annoying to the
human ear can be remedied by selecting proper dimensions and
by avoiding continuous flat and smooth walls. The continuity may
be broken by having a number of windows or by introducing
irregularities in the surface of walls such as artistic engravings or
by suspending thick curtains. The sound is thus scattered
irregularly when the walls are uneven and thus, in this way, the
formation of echoes can be avoided.
When the reflecting surface (wall, cliff etc.) is a little less than 17
meters away from the source producing sound, then, echo follows
so closely upon the direct (or original) sound that these two
cannot be distinguished as separate (or distinct) sounds. One
merely gets the impression (or sensation) that the original sound
has been prolonged. This effect is known as reverberation. Like
echoes, reverberations also cause (or give rise to) general

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confusion of the sound impressions on the ear. The same remedy
as mentioned above for echoes can minimize this defect also.
It has been seen (or noticed) that concert halls with no
reverberation at all are not liked by speakers and singers because
it is felt as if they are performing in the open. Such halls are
acoustically dead. Therefore, some degree of reverberation is
useful in order to improve the hearing.
An empty hall exhibits these defects (of echo or reverberation)
more strongly than the same hall full of audience. Human bodies
and the clothes thereof serve as good absorbents of sound which,
in absence of audience, would have been reflected strongly.
Large curved walls produce a focusing of the sound waves at
certain spots only and sound is not heard clearly at other places.
Such walls should, therefore, be avoided in designing a lecture
hall.
Intensity and Loudness of Sound
We know that the compressional (or longitudinal) waves transmit
energy. Accordingly, sound waves being the compressional
waves also carry energy away from the source. The vibrating
source does work on the surrounding medium and this work
appears as the energy of the waves. The energy transmitted per

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second through a unit area by the sound waves is called the
intensity of the sound waves.
It may be pointed out here that the intensity of sound is purely a
physical quantity. It can be measured accurately. It is independent
of the ear. On the other hand, a second quantity, i.e., loudness is
the magnitude of auditory sensation produced by sound in air. It
does depend upon the intensity, but, it also depends upon the
ear. The human ear is no doubt a very sensitive detector of
sound. It can record the least intense sound (10-12
watt m-2
) which
is one billionth of the maximum sound Intensity that can be heard
without pain. However, it is seen that ear operates on an
approximately logarithmic scale rather than responding linearly to
the sound intensity. This is called Weber-Fechner Law.
Loudness
It is the property of sound by which loud and faint sounds are
distinguished. The loudness depends upon the following factors.
1. Amplitude of the vibrating body.
2. Surface area of the vibrating body.
3. Distance between the sounding body and listener.
4 Direction of Wind, and
5 Density of Medium.

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1 Amplitude of the Vibrating Body
If the amplitude of the vibrating body is large, sound will be loud.
But, if the amplitude is small, the sound will be faint, e.g. the loud
sound of sitar when the wires are plucked violently and loud
sound of drum when we beat it forcefully.
2 Surface Area of Vibrating Body
If the surface area of the vibrating body is large, sound will be
loud. But, if the surface area is small, the sound will be faint. The
loudness of sound of school bell is more than that of house bell,
because, the surface area of school bell is more than that of
house bell.
3 Distance of the Sounding Body
By increasing the distance between the sounding body and the
listener, the loudness is decreased. However, by decreasing the
distance, the loudness is increased. A faint sound is heard when
train is far away from us. But, the sound will be the loudest when
the train passes by us.
4 Direction of Wind
If the sound waves travel in the direction of wind, a loud sound is
heard. But, if the sound is travelling against the wind, a faint
sound will be heard.

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5 Density of Medium
Loudness of the sound also depends upon the density of the
medium through which the sound is travelling. A faint sound is
heard if it is passed through hydrogen gas. But, a loud sound is
produced, if, it is passed through the air because the density of air
is more than that of hydrogen gas.
Thus, the larger the density of the medium, the louder is the
sound. If the density is less, faint sound is heard.
Musical Interval
The ratio of the frequencies of two notes is called the musical
interval between them.
Musical Sound and Noise
Ordinarily, sound which produces a pleasing (or attractive)
sensation on the human ear is called a musical sound, whereas,
one which produces a jarring or a displeasing (annoying) effect on
the human ear is called a noise. The conditions necessary for the
production of a musical note are that sound waves should
succeed each other
(1) at regular interval,
(2) in quick succession, and
(3) without sudden changes in loudness.

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Thus, in other words, musical sounds have a particular frequency
and amplitude and these sounds have regular shape and there is
no abrupt change in the amplitude and frequency of these sound
waves.
Examples of musical sounds are: the sound produced by a tuning
fork, by plucking the string of sitar, the sound of a flute, violin, etc.
and the sound produced by blowing into an open or closed organ
pipe.
Characteristics of Musical Sound
Musical sound has following characteristics:
1 Loudness
2. Pitch
3. Quality
Noise, on the other hand, are sounds of very short duration
having no periodicity and their character is changing.
Thus, in other words, these sounds (noise) have no regular
frequency or amplitude. Also, their amplitudes and frequencies
have irregular and abrupt changes.
Some familiar (or known) examples of noise are: the jingling of
keys, clapping of hands, the report of a gun, the roar of street

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traffic, the rattling of wheels and the sound of a hammer striking
an anvil.
The physical difference between a musical sound and a noise is
clear from the figure below.
Fig: (a) Musical sound, (b) Noise.
The upper curve is uniform, regular and represents a musical
sound. The lower curve is irregular and shows sudden changes in
loudness and represents a noise. Hence, a musical sound is that
which is produced by a series of similar impulses following each
other regularly, at equal intervals, in quick succession, without
any sudden changes in loudness.
Reflection of Sound
We know that sound waves from a source travel in all directions
and when they come across another surface, the sound waves

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undergo reflection and travel in different directions. The sound
heard after reflection is called an echo.
Fig: Reflection from a wooden board
Experiment
Take a long PVC pipe and cut it into two equal parts. Hold the two
parts against a smooth surface. Place a watch at the open end of
one of the parts of the pipe and ask a person to place his ear
against the open end of the second part of the pipe. Tell the
person to slightly move the part of the pipe sideways till clear
ticking of the watch is heard. Place a big cardboard sheet
between the two parts of the pipe, so that, the sound does not
reach the ear through any other path. Measure the angles that the
two parts of the pipe make with the normal at the point of
incidence. The angle of incidence will be equal to the angle of
reflection.

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A sound whispered against the wall on one side of the whispering
gallery in the Shah Jehan mosque Thatta can be heard clearly on
the other side. Being circular in shape and made up of stones, the
walls reflect the sound of the whisperer all around the gallery and
it concentrates at the opposite side 32.6m away.
Another application of reflection of sound is observed in the use of
whispering tube and stethoscopes. A faint sound of the heart
throb or the inhaling and exhaling air by the lungs is fed into a
narrow flexible tube. This sound travels through the tube and
reaches the ear drum after several reflections.
Carbon Microphone
The carbon microphone has a thin metal plate, called a
diaphragm, suspended in front of a packing of carbon granules.
When these granules are in a compressed form, the air space or
inter-granular distance decreases and so the resistance offered
by the layer of carbon granules to the flow of current decreases.
More current flows when the granules are in the compressed
state than when the distance between the granules is relatively
large. If someone speaks in front of a microphone, the
compression and rarefaction, that constitute a sound wave, cause
the diaphragm to vibrate. These vibrations increase or decrease
the pressure on the carbon granules very rapidly. Since, the

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granules are part of the circuit, so the current fluctuates in
harmony with the sound waves.
Telegraphy
The electric telegraph is a device for sending and receiving
messages between two distant areas by an electric current
flowing through a wire connecting the two areas.
Telegraphic Circuit
In its simplest form, an electric telegraph consists of an electric
battery connected through tapping key (called the sender) to an
electric buzzer (called the receiver).
Only one wire is needed between the sender and the receiver as
the circuit is completed by connecting their other ends to the
earth. The earth is usually moist a few feet below the surface and
acts as a good conductor.
When the tapping key is pressed, the receiver produces a buzzing
sound.
Telephone
In telegraphy, a message can be sent and received at the other
end of a telegraph network by experts who know the International

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Morse Code very well. This mode of communication is slow and
time consuming. Thus, there was a need to have such a device
by which speech could be transported over a long distance
directly from the speaker to the listener. The telephone, which
sends sound to a distant place, is the appliance that fulfills this
need. This is based on the same principle as that of the telegraph,
i.e., sending and receiving messages between two distant places
by an electric current flowing through the wires connecting the two
places.
In the telephone system, invented by Graham Bell in 1876, a
carbon microphone replaces the tapping key and a magnetic
earphone takes place of the buzzer.
It may be pointed out that two wires are used for telephone,
whereas, in telegraphy, one wire carries the current while the
earth connections complete the circuit. The reason is that the
earth connections, if also made in a telephone network, would
cause so much noise and distortion in the original sound that the
message would become unintelligible.
Later on, scientists developed telephone systems using optical
fibres instead of ordinary copper wires. This had improved very
much the quality of sound. Sound waves are converted into
electrical fluctuations which, in turn, are changed into light pulses

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with the help of a transducer (a device that converts variation of
one quantity into another e.g., electrical variations into light
pulses). These light pulses travel through optical fibres which are
as thin as hair. On the receiving end, the light pulses are changed
back into electrical variations by another transducer and then
back into sound waves by the earphone.
Telephone Receiver
The telephone receiver is a device which converts electrical
energy into sound energy.
Pitch and Quality of Sound
The characteristic of sound by which we can distinguish between
grave and shrill sound of same loudness is called pitch.
If a number of tuning forks of different frequencies are sounded
one after the other, then, anyone with a normal ear can
distinguish between sounds produced by these forks even if these
are of equal loudness. Sound produced by a tuning fork of high
frequency will be shrill while that produced by a fork of low
frequency will be grave. The characteristic of sound by which a
shrill sound can be distinguished from a grave one is known as
the pitch of the sound. It depends upon frequency, the greater the
frequency, the higher the pitch and lower the frequency, the lower
the pitch. The pitch of women is higher than the pitch of men.

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Therefore, the voices of women are shriller as compared to the
voices of men. Sometimes, pitch and frequencies are considered
as synonymous, but, in fact, pitch is a sensation depending upon
frequency.
It is a common experience that a note of given pitch and loudness
sounded on piano is easily distinguished from one of exactly the
same pitch and loudness played, for example, on violin. It is
because the quality of the two notes is different.
A string under tension, when excited, vibrates not only with its
fundamental frequency but also several other harmonics are
produced at the same time. The resultant vibration is found by
adding together the waves of the various vibrations present.
In the figure below,
Fig: Resultant Waveform when two Waves are combined.

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the resultant vibration of
(1) fundamental and second harmonic, and
(2) fundamental and third harmonic are illustrated. It is seen that
the presence of different harmonics affects the waveform of the
note.
The quality of the sound depends upon the waveform of the
resultant and is controlled by the number and relative intensities
and phase of the harmonics that are present. The resultant
waveforms shown in the above figure will have different effects on
the ear even though they have the same pitch and loudness.
They will, however, give rise to notes of different qualities.
The persons speaking with the same loudness may have the
same fundamental frequency of vibration, but, they differ in their
harmonics or overtones which determine the quality of sound. It
means that the qualities of their voices are different. Hence, they
can be recognized due to the difference of quality in their voices.
Beats
When two notes of nearly equal pitch are both sounded together,
then, a regular rise and fall occurs in the loudness of the tone
heard. These alternations in loudness are called beats.
For example, if two tuning forks of slightly different frequencies

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are struck simultaneously, then, we hear a sound of alternately
high and low intensity, i.e. we will not hear the two separate notes
but a single note which rises and falls in intensity. A rise and a fall
in intensity constitutes one beat, i.e. in other words, the periodic
alternations between maximum and minimum loudness are called
beats.
Thus, the type of interference in which two waves of different
frequencies are involved is known as beats. In this case, when,
two waves are observed at a given point, they are periodically in
or out of step with each other. That is, there is an alternation in
time between constructive and destructive interference and this
phenomenon is known as interference in time.
Beats can also be defined as the periodic variation in intensity at
a given point due to the superimposition of two waves having
slightly different frequencies.
Number of beats heard per second called beat frequency is equal
to difference of frequencies of the two sound waves.
The maximum beat frequency that a normal human ear can
detect is 7 beats per second.
The phenomenon of beats is used in finding the unknown
frequencies and also in tuning the musical instruments.

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Buzzer
The buzzer consists of an electromagnet connected through a
movable iron bar which is held against a contact point by a light
spring. When tapping key is pressed, a current starts flowing
through the coil of the electromagnet and the bar is pulled
towards the electromagnet. This breaks the circuit between the
bar and the contact point, resulting in the stoppage of current
flow, and the bar is no longer attracted. The spring then pulls the
bar back to the contact point and the current again starts flowing.
Thus, by pressing the tapping key, the iron bar oscillates and a
buzzing sound is produced. The interval between two buzzing
sounds can be controlled by the interval between pressing the
tapping key. A short interval is known as a dot (.) while a long
interval is termed as a dash (-). By using International Morse
Code, messages can be sent from one place to another distant
place.

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Earphone
The magnetic earphone has a thin steel plate suspended in front
of an electromagnet. When, the current in the circuit fluctuates,
the field of the electromagnet changes accordingly. The steel
plate, therefore, experiences fluctuating force of attraction and
vibrates in the same fashion as the current in the circuit changes.
Sound waves are converted into electrical fluctuations by the
microphone at one end and the electrical fluctuations are
converted into sound waves by the earphone at the other end.
Sonometer
A sonometer is a device (or an instrument) which is generally
used to determine (or calculate) the unknown frequency of a
vibrating body (tuning fork) and to verify the laws of transverse
vibration of strings.
Principle
If a stretched string is excited by a small periodic force having
frequency equal to any of the quantized frequencies of the string,
then, the phenomenon of resonance will take place and stationary
waves will be set up on the string.

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Construction
It consists of a rectangular wooden box over which a steel wire is
stretched. One end of the wire is fixed to a peg and the other end
passes over a pulley. This end carries a hanger on which slotted
weights can be slipped (or added) so as to vary the stretching
force (i.e. tension) in the string (or wire) as shown in the figure
below.
Fig: The Sonometer
Two sharp wedges C and D are placed below the wire. A
horizontal graduated scale in millimeters is fixed below the wire
on the box in order to read (or measure) the length of the vibrating
segment.
Determination of Frequency
To determine (or find) the frequency of a tuning fork, the steel
wire of the sonometer is stretched with a load of a few kilograms
on the hanger so that the wire remains taut. A V-shaped paper
rider is placed in the middle of the wire between the two sharp
wedges. The tuning fork, whose frequency is to be determined, is

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struck gently with a rubber pad and its stem is placed gently on
the sonometer board.
The distance between the wedges is adjusted (by changing) till
the rider flies off (or falls down). The wire between points C and D
is now vibrating in one loop in resonance with the tuning fork and
hence produces a note of the same frequency. It means that the
frequency of the vibrating loop is equal to the frequency of the
tuning fork. Thus, resonance is produced and the rider falls down.
The length of the wire 'ℓ' between the sharp wedges C and D is
measured and mass in the hanger is also noted. A length equal to
50 cm of the wire is cut and weighed from which the mass per unit
length is calculated. Let T be the stretching force (tension), then,
the frequency 'f' is determined (or calculated) by the following
relation:
____
f = 1/2ℓ √T/m
Here, T = weight suspended