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What is the difference between the loudness and intensity of sound? Derive the relation between the two.

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Ans.  LOUDNESS

It is the characteristics of sound by which loud and feint sounds can be distinguished.

INTENSITY OF SOUND -

Sound energy passing per second through a unit area held perpendicular to

Solid direction of propagation of sound waves is called intensity of sound.

Unit: The SI unit of intensity of sound is watt per square metre (Wm  ).

TaWeH.2

   

Sources of Sound

Intensity (WnT2)

Intensity level (dB)

   

Nearby jet airplane

103

150

   

Jackhammer / Fast

101

130

   

Train Siren

10°

120

   

Lawn mover

10^

100

   

Vacuum cleaner

1CT5

70

   

Mosquito buzzing

io-8

40

   

Whisper

to-9

30

   

Rusting of leaves

io~11

10

   

Faintest audible

ft *5

   

sound i.e. Threshold

10~12

0

Relation Between Loudness and Intensity of Sound

The loudness (L) of a sound is directly proportional to the logarithm of intensity.

i.e.  L oc log I

or   L=Klogl ......    (1)

where K is constant of proportionality.

Let L0 be the loudness of the faintest audible sound of intensity I0 and L be the loudness of an unknown sound of intensity 1, then by Eq. (1), we can write

L0 = KlogI0 ......    (2)

Subtracting Eq. (1) from Eq. (2), we get

L-L0 = KlogI-Klogl0 = K (log 1 - log 10) Since ( log a - log b - log t), therefore

L-L0=Klogf

Equation (3) give%the relation between loudness and intensity of sound.
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