First slide

Travelling wave

Question

A small speaker delivers 2 W of audio output at what distance from the speaker will one detect 120 dB intensity sound (Given reference intensity = $10^{- 12} W / m^{2})$

Moderate

A

10 cm
B

30 cm
C

40 cm
D

20 cm

Solution

$L o u d n e s s o f s o u n d i s g i v e n b y d B = 10 \log I / I_{0} \Rightarrow 120 = 10 \log (I / I_{0}) \Rightarrow 120 = 10 \log (I \times 10^{12}) ∴ I = 1 W / m^{2} A l s o, I = P / 4 π r^{2} \Rightarrow I = \frac{2}{4 π r^{2}} \Rightarrow r^{2} = \frac{1}{2 π} \Rightarrow r = \sqrt{\frac{1}{2 π}} m = 0.399 m \Rightarrow r = 40 c m$

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