First slide

Travelling wave

Question

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

Easy

A

Zero
B

54 dB
C

64 dB
D

44 dB

Solution

$I \propto \frac{1}{r^{2}} \Rightarrow \frac{I_{2}}{I_{1}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{2^{2}}{{(40)}^{2}} = \frac{1}{400} \Rightarrow I_{1} = 400 I_{2}$
Intensity level at point 1, $L_{1} = 10 \log_{10} (\frac{I_{1}}{I_{0}})$
and intensity at point 2, $L_{2} = 10 \log_{10} (\frac{I_{2}}{I_{0}})$
$∴ L_{1} - L_{2} = 10 \log \frac{I_{1}}{I_{2}} = 10 \log_{10} (400)$
$\Rightarrow L_{1} - L_{2} = 10 \times 2 .602 = 26$
$L_{2} = L_{1} - 26 = 80 - 26 = 54 dB$

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