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30 seconds of exposure to 115 dB sound can damage your hearing, but a much quieter 94 dB may begin to cause damage after 1 hour of continuous exposure. You are going to an outdoor concert, and you'll be standing near a speaker that emits 50 W of acoustic power as a spherical wave. What minimum distance should you be from the speaker to keep the sound intensity level below 94 dB?

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usmanbiu

Answer:

39.8 m ≈ 40 m

Explanation:

power (P) = 50 W

sound intensity level ([tex]p[/tex]) = 94 dB

the distance (r) can be gotten from the equation I = [tex]\frac{power}{4nr^{2} }[/tex] (take not that π is shown as [tex]n[/tex])

making r the subject of the formula we have r = [tex]\sqrt{\frac{power}{4nI} }[/tex]   (take not that π is shown as [tex]n[/tex])

But to apply this equation we need to get the value of the intensity (I)

  • we can get the intensity (I) from the formula sound intensity level ([tex]p[/tex]) = 10 log₁₀[tex](\frac{I}{I'})[/tex]
  • rearranging the above formula we have intensity (I) = [tex]I' x 10^{\frac{p}{10} }[/tex]
  • I' = reference intensity = 1 x[tex]10^{-12} W/m^{2}[/tex]
  • now substituting all required values into the formula for intensity (I)
  • I = [tex]1 x 10^{-12} x 10^{\frac{94}{10} }[/tex] = 0.00251 [tex]W/m^{2}[/tex]

now that we have the value of the intensity (I)  we can substitute it into the formula for the distance (r)

distance (r) = [tex]\sqrt{\frac{power}{4nI} }[/tex]

r = [tex]\sqrt{\frac{50}{4x3.142x0.00251} }[/tex] = 39.8 m ≈ 40 m

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