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Question

# One decibel change in loudness is equal to:

A

36 % change in loudness of sound

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B

26 % change in intensity of sound

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C

26 % change in loudness of sound

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D

36 % change in intensity of sound

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Solution

## The correct option is B 26 % change in intensity of sound Since, L = 10 log10(I) dB, where 'L' is loudness and 'I' is intensity. Now, L1 = 10 log10(I1) dB L2 = 10 log10 (I2) dB L2 - L1 = 10( log10(I2 ) - log10(I1 )) = 10 log10( I2I1 ) dB Now if change in loudness is 1 dB, L2 - L1 = 1 dB So, 10 log10( I2I1 ) = 1 ⇒ log10( I2I1 ) = 110 ⇒ I2I1 = antilog (0.1) = 1.26 Now % change = I2−I1I1 × 100 = 26 %

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