Question

One decibel change in loudness is equal to

• A. 36% change in loudness of sound
• B. 26% change in intensity of sound
• C. 26% change in loudness of sound
• D. 36% change in intensity of sound

Answer 1

The correct option is B

26% change in intensity of sound

Since, L = 10 ${log}_{10}$($I$) dB, where 'L' is loudness and 'I' is intensity.

Now, $L_1$ = 10 ${log}_{10}$($I_1$) dB

$L_2$ = 10 ${log}_{10}$ ($I_2$) dB

$L_2$ - $L_1$ = 10( ${log}_{10}$ ($I_2$ ) - ${log}_{10}$ ($I_1$ )) = 10 ${log}_{10}$ ( $\frac{I2}{I1}$ ) dB

Now if change in loudness is 1 dB,$L_2$ - $L_1$ = 1 dB

so, 10 ${log}_{10}$ ( $\frac{I_2}{I_1}$ ) = 1

$\Rightarrow$ ${log}_{10}$ ( $\frac{I_2}{I_1}$ ) = $\frac{1}{10}$

$\Rightarrow$ $\frac{I_2}{I_1}$= antilog (0.1) = 1.26

Now % change = $\frac{I_2-I_1}{I_1}$ x 100 = 26%