An electronic point source emits sound isotropically at a frequency of 3 × 103 H

Question

An electronic point source emits sound isotropically at a frequency of 3 × 103 Hz and a power of 30 watts. A small microphone has an area of 0.74 cm2 and is located 183 meters from the point source.

1. What is the sound intensity at the microphone ? I =

2. What is the power intercepted by the microphone? Pin =

3. How many minutes will it take for the microphone to recieve 0.1 Joules from this sound? T =

4. What is the sound intensity level at the microphone from this point source? = && What would be the sound intensity level at the microphone if the point source doubled its power output? =

Explanation / Answer

part 1: Intensity I = power/area

I = 30/(4pi r^2)

I = 30/(4 *3.14 * 183^2)

I = 7.13 *10^-5 W/m^2
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Power P = I A

P = 7.13 *10^-5 * 0.74 *10^-4

P = 5.27 *10^-9 Wattts

----------------------------

3) E = Pin*t

t = E/pin

t = 1/(5.27*10^-9)

t = 1.89* 10^8 s

t = 3.16*10^6 min

-----------------------------

4) intensity Level L = B = 10dB*log(I/Io)

= 10 dB*log(7.13*10^-5/10^-12)

= 78.5 dB
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5)

B = 10dB*log(2*I/Io)

B = 10 dB*log(2*7.13*10^-5/10^-12)

B = 81.54 dB

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