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  • A small speaker delivers of audio output. At what distance from the speaker w

A small speaker delivers \small 8 \mathrm{w} of audio output. At what distance from the speaker will one detect \small 140 \mathrm{~dB} intensity sound? [Given reference intensity of sound as \small \left.10^{-14} \mathrm{w} / \mathrm{m}^2\right]

Option: 1

7.95 cm


Option: 2

2.25 cm


Option: 3

3.67 cm


Option: 4

2.98 cm


Answers (1)

best_answer

\begin{aligned} & L=10 \log _{10}\left(\frac{I}{I 0}\right) \\ & 140=10 \log _{10}\left(\frac{I}{I 0}\right) \\ & 14=\log 10\left(\frac{I}{10^{-14}}\right) \\ & \frac{I}{10^{-14}}=10^{14} \\ & I=1 \mathrm{~W} / \mathrm{m}^2 \end{aligned}

\begin{aligned} & I=\frac{\rho}{4 \pi r 2} \\ & r=\sqrt{\frac{P}{4 \pi I}}=\sqrt{\frac{8}{4 \times \pi \times 1}}=\sqrt{\frac{2}{\pi}} \\ & r=\frac{\sqrt{2 \times 100}}{\sqrt{3 \cdot 14}} \end{aligned}

\begin{aligned} & r=\frac{10 \times 1.414}{\sqrt{3.14}}=\frac{10 \times 1.414}{1.78}=\frac{14.14}{1.78} \\ & r=7.95 \mathrm{~cm} \end{aligned}

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seema garhwal

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