First slide

Travelling wave

Question

A person speaking normally produces a sound intensity of 40 dB at a distance of 1 m. If the threshold intensity for reasonable audibility is 20 dB, the maximum distance at which he can be heard clearly is

Difficult

A

4 m
B

5 m
C

10 m
D

20 m

Solution

$dB = 10 \log_{10} (\frac{I}{I_{0}})$ ; where $I_{0} = 10^{- 12} {Wm}^{- 2}$
Since $40 = 10 \log_{10} (\frac{I_{1}}{I_{0}}) \Rightarrow \frac{I_{1}}{I_{0}} = 10^{4}$ ....(i)
Also $20 = 10 \log_{10} (\frac{I_{2}}{I_{0}}) \Rightarrow \frac{I_{2}}{I_{0}} = 10^{2}$ ....(ii)
$\Rightarrow \frac{I_{2}}{I_{1}} = 10^{- 2} = \frac{r_{1}^{2}}{r_{2}^{2}} \Rightarrow r_{2}^{2} = 100 r_{1}^{2} \Rightarrow r_{2} = 10 m$
${∵ r_{1} = 1 m}$

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