Question

Four sources of sound each of sound level 10 dB are sounded together in phase, the resultant intensity level will be :
($lo{g}_{10}2=0.3$)

• A. 40 dB
• B. 26 dB
• C. 22 dB
• D. 13 dB

Answer 1

The correct option is C 22 dB

Let the intensity of each source be $I$ and the resultant intensity of four sources be $I_R$.

Resultant intensity of two same sources is equal to $4$ times the intensity of one source, i.e $I^{\prime }=4I$

Thus resultant intensity of $4$ same sources $I_R=4\left(4I\right)=16I$

Loudness of a sound $L=10lo{g}_{10}\frac{I}{I_o}$

$⟹L_R-L=10lo{g}_{10}\frac{I_R}{I}$ where $L_R$ is the resultant loudness

$L_R-10=10lo{g}_{10}\frac{16I}{I}$

$L_R-10=10\times 4lo{g}_{10}2=10\times 4\times 0.3$

$L_R-10=12$

$⟹L_R=22dB$