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 ${log}_{10}$( $\frac{I_2}{I_1}$ ) 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 = $\frac{I_2-I_1}{I_1}$ $\times$ 100 = 26 %