Question

what will be the resultant intensity level when four sources of sound each of sound level 10dB are sounded togather in phase ??

( log₁₀2 = 0.3)

Answer 1

Dear student,

The sound level (L) of each source is 10dB. Let corresponding intensity of sound is I.
So, $L=10\log \frac{I}{I_0}=10\mathrm{dB}$
Resultant intensity of 4 sound sources,
$I\text{'}=4I$
Corresponding sound level,
$$\begin{gathered} L\text{'}=10\log \frac{I\text{'}}{I_0}=10\log \frac{4I}{I_0}=10\log 4+10\log \frac{I}{I_0} \\ \Rightarrow L\text{'}=10\log 2^2+10\log \frac{I}{I_0} \\ \Rightarrow L\text{'}=20\log 2+10\log \frac{I}{I_0} \\ \Rightarrow L\text{'}=20\times 0.3+10=16\mathrm{dB} \end{gathered}$$

Regards.