Question

The sound intensity level at a point $4m$ from the point source is $10dB$, then the sound level at a distance $2m$ from the same source will be :

• A. $26dB$
• B. $16dB$
• C. $23dB$
• D. $32dB$

Answer 1

The correct option is B $16dB$

Sound level at $A$ is $\perp o\perp B$

If the intensity of sound at $A4cm$ away from the source is $I_A$

then.

$\perp o=10\log \frac{I_A}{I_o}$ Where $I_o={10}^{-12}w{m}^{-2}$

$\Rightarrow \perp =\log \frac{I_A}{{10}^{-12}}$

$\Rightarrow \frac{I_A}{{10}^{-12}}=10$

$\Rightarrow I_A={10}^{-11}w{m}^{-2}$

If the source (s) is emmitting the sound energy of power $P$

$I_A=\frac{P}{4\times (4{)}^2}$

$\Rightarrow P={10}^{-11}\times 64\pi$ $w$

$\Rightarrow$ Intensity of sound $\left(I_B\right)$ ar point $B,2m$

$I_B=\frac{P}{4\pi (2{)}^2}$

$I_B=\frac{64\pi \times {10}^{-11}}{16\pi }10m^{-2}$

$\Rightarrow I_B=4\times {10}^{-11}w{m}^{-2}$

$\Rightarrow$ Sound level at $2m=10\log \left(\frac{I_B}{I}\right)$

$=10\log \left(\frac{4\times {10}^{-11}}{{10}^{-12}}\right)$

$=10\log 40$

$=16.02$

Hence Sound level at $2m$ from sourceis $16dB$