Page 9 - 10-phy-11 Sound

11. Sound eLearn.Punjab

Let L0 be the loudness of the faintest audible sound of For your information
intensity I0 and L be the loudness of an unknown sound of
intensity I, then by Eq. (11.1), we can write A sound wave with a frequency of 3500
Hz and an intensity of 80 dB sounds
L0= K log I0 .......... (11.2) about twice as loud to us as a sound of
Subtracting Eq. (11.2) from Eq. (11.1), we get 125 Hz and 80 dB. It is because our ears
are more sensitive to the 3500 Hz sound
L - Lo = K (log I - log I0 ) = K log l/Io than to the 125 Hz. Therefore intensity

by itself does not mean loudness.

This difference,(L- L0), between the loudness L of an unknown Loudness is how our ears detect and
our brain perceives the intensity of
sound and the sound waves.
Table 11.1
loudness Lo
Intensity Intensity
Source of Sound (Wm-2) level (dB) is called the intensity level of the unknown sound.

Nearby jet airplane 103 150 Therefore, the intensity level of an unknown sound is

Jackhammer/Fast Train 101 130 given by

Siren 100 120 Intensity level = K log l/Io .......... (11.3)
Lawn Mover 10-2 100

Vacuum Cleaner 10-5 70
Mosquito buzzing
10-8 40 The value of K depends not only on the units of I and

Whisper 10-9 30 I0 but also on the unit of intensity level. If intensity I
Ruslting of leaves 10-11 10 of any unknown sound is 10 times greater than the
Faintest audible sound 10-12 0 intensity I0 of the faintest audible sound i.e., I =10 I0
i.e. Threshold
and the intensity level of such a sound is taken as unit,

called bel, the value of K becomes 1. Therefore, using K =1, Eq. (11.3) becomes

Intensity level = log l/Io (bel) .......... (11.4) For your information

bel is a very large unit of intensity level of a sound. Logarithmic scale Linear
Generally, a smaller unit called decibel is used. Decibel
is abbreviated as (dB). It must be remembered that 1 Decibels (dB) Scale
bel is equal to 10 dB. If the intensity level is measured 0 Amplitude (m)
in decibels, Eq. (11.4) becomes 20
40 1
Intensity level = 10 log l/Io (dB) ..........(11.5) 60 10
80 100
Using Eq. (11.5), we can construct a scale for measuring 1,000
the intensity level of sound. Such scale is known as 100 10,000
“decibel scale”. The intensity level of different sounds 120 100,000
in decibel is given in table 11.1. 1,000,000

The decibel scale is a logarithmic measure of the
amplitude of sound waves. In a logarithmic scale,
equal intervals correspond to multiplying by 10

instead of adding equal amounts.

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