Question

(a) The power of sound from the speaker of a radio is $20mW$ . By training the knob of volume control the power of sound is increased to $400mW$ . What is the power increase in dB as compared to original power ? (b) How much more intensive is an $80dB$ sound than a $20dB$ whisper ?

Answer 1

$a)$ As intensity is the power per unit area, for a given source $P\mu I$. If $L_1$ and $L_2$ are the initial and final loudness levels, then we have
$L_2-L_1=10log\left(I_2/I_1\right)$
The increase in loudness level is

$\Delta L=10log\frac{P_2}{P_1}=10log\frac{400}{20}$
$\Rightarrow$ $\Delta L=10\left[log20\right]=13dB$
$\left(b\right)$. Increase in loudness level of sound is
$L_2-L_1=10log\left(I_2/I_1\right)$
$\therefore$ $80-20=10log\left(I_2/I_1\right)$
$\Rightarrow$ $6=log\left(I_2/I_1\right)$
$\Rightarrow$ $\left(\frac{I_2}{I_1}\right)={10}^6$