Q. Intensity level $200\ cm$ from a source of sound is $80\ dB.$ If there is no loss of acoustic power in air and intensity of threshold hearing is $10^{- 12}Wm^{- 2}$ then, what is the intensity level at a distance of $4000\ cm$ from source

A) Aero
B) $54\ dB$
C) $64\ dB$
D) $44\ dB$
Explanation

(b) $I \propto \frac{1}{r^{2}} \Rightarrow \frac{I_{2}}{I_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{2^{2}}{(40)^{2}} = \frac{1}{400} \Rightarrow I_{1} = 400I_{2}$
Intensity level at point $1,\ L_{1} = 10\log_{10}\left( \frac{I_{1}}{I_{0}} \right)$
and intensity at point $2,\ L_{2} = 10\log_{10}\left( \frac{I_{2}}{I_{0}} \right)$
$\therefore L_{1} - L_{2} = 10\log{\frac{I_{1}}{I_{2}} = 10\log_{10}{(400)}}$
$\Rightarrow L_{1} - L_{2} = 10 \times 2.602 = 26$
$L_{2} = L_{1} - 26 = 80 - 26 = 54\ dB$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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