# NTSE physics question Decibel (dB) is a unit of .loudness of sound. It is defined in a manner such that when amplitude of sound is multiplied by a factor of √10 , the: decibel level increases by 10 units. Loud music of 70 dB is being played at a function. To reduce the loudness to a level of 30 dB, the amplitude of the instrument playing music has to be reduced by a factor of 1. 10 2. 10√10 3. 100 Please explain! Thanks

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2015-10-10T02:34:01+05:30

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Sound loudness in decibel =  dB = 120 + 10 * Log_10  I_s
I_s = intensity of sound.          logarithm to base 10.

If amplitude is multiplied by a factor of √10, then the intensity is multiplied by (√10)² = 10.

So  loudness in dB'  = 120 + 10 * [Log (√10)² + Log Is]  =  10 +  dB

So if  70 dB loud music is played at a function,  if it to be reduced to 30 dB, its amplitude is reduced by a factor of n.

then  dB' = 120 + 10 * Log  ( I_s/ n²)  = 120 + 10 * Log I_s  - 10 Log n²
= dB - 20 Log n
dB - dB'  = 20 Log n

70 - 30 = 20 log n
n  =  10²  = 100
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as decibel level changed by  40 dB, ie., 4 times 10 dB,  so intensity changes by 10^4.   Amplitude changes  as square root of intensity,  so 10².