What Is the Power of a Sound Source Emitting 80dB at 30m?

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SUMMARY

A sound source emitting 80dB at a distance of 30 meters has a calculated power output of 1.13 watts. This conclusion is derived using the formula for sound intensity, where 80dB corresponds to an intensity of 10^(-4) W/m². The power is determined by the equation P = I * A, with A being the surface area of a sphere (4πr²) at the given distance. Despite the calculated power, the answer does not match the provided options, indicating a possible error in the question's answer choices.

PREREQUISITES
  • Understanding of sound intensity and decibels (dB)
  • Familiarity with the formula for sound intensity: I = P/A
  • Knowledge of the reference intensity level Io = 10^(-12) W/m²
  • Basic geometry of spheres for calculating surface area
NEXT STEPS
  • Study the relationship between sound intensity and decibel levels in detail
  • Explore the derivation of sound power calculations from intensity
  • Investigate common errors in sound-related exam questions
  • Learn about the implications of sound dispersion in different environments
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Students preparing for physics exams, educators teaching acoustics, and anyone interested in the practical applications of sound intensity calculations.

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Homework Statement



A sound source emits uniformly in all directions. It produces a sound level of 80dB at a distance 30m. What is the power of the emitting source. (W)

Homework Equations



dB = 10log(I/Io)

Io = 10^(-12) W/m^2

I = P/A


The Attempt at a Solution



80dB = 10^(-4) W/m^2

sound disperses in a sphere..

I = P/(4*pi*r^2)

P = 10^(-4)*4*pi*(30)^2

= 1.13W


This answer is not listed, although multiples of it, 2.26, 3.39, 4.52 are choices.
 
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oo well, I think you did it right. I also get same thing =P
See the answers carefully , you will notice that a) is 13 and things on left side are erased, so it must be 1. on the left!

Anyways, good luck with the exam tomorrow!

P.S. funny how I also got stuck on the same question.
 
ah i see it. I found it odd that I was getting a wrong answer for the easiest question on the exam. thought maybe Rohan was playing tricks on me.

yeah good luck yourself (seems to be a good share of waterloo students here), no more bell curve anymore to take away the wrong answers!
 

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