Question

When you wear protective earmuffs, the sound level is decreased by 30 dB. By how much does the perceived loudness decrease?

Answer 1

We perceive one sound to be twice as loud as another one when they are about 10 dB apart . So, if sound level is decreased by 30 dB then the perceived loudness will become 1/8 times of initial value (i.e. decreased by 3 times of initial value).

The sound level is measured in decibel (a logarithmic scale), and is given by

  

Where, I is intensity of the sound

   is reference intensity

Given ,

or,

or,

or,   

or,

Hence, the intensity of sound will become 10^-3 times of initial intensity. So, loudness will become 2^-3 (i.e. 1/8) of its initial value.

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