Calculate Intensity of Sound Waves at 3.0 m from Source

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SUMMARY

The discussion focuses on calculating the intensity of sound waves emitted from a source with a power output of 80W at a distance of 3.0 meters. The intensity at this distance is determined to be 0.71 W/m², and the intensity level is calculated to be 118.51 dB. For part (c), the user attempts to find the distance where the intensity is one-fourth of the initial intensity, arriving at a distance of 7.173 meters, which requires verification of calculations involving the formula I = P / (4πr²).

PREREQUISITES
  • Understanding of sound intensity and intensity level calculations
  • Familiarity with logarithmic functions, specifically in the context of sound levels
  • Knowledge of the formula for intensity from a point source: I = P / (4πr²)
  • Basic arithmetic skills for verifying calculations involving π and distance
NEXT STEPS
  • Review the derivation of the intensity formula I = P / (4πr²)
  • Learn how to calculate sound intensity levels using the formula B = 10 log(I/I₀)
  • Explore the implications of distance on sound intensity and its practical applications
  • Practice solving problems involving sound intensity at various distances from a source
USEFUL FOR

Students studying physics, particularly those focusing on acoustics and sound wave behavior, as well as educators seeking to reinforce concepts related to sound intensity calculations.

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Homework Statement


A small source emits sound waves with a power output 80W.
a) find the intensity at a point 3.0m from the source. (0.71W/m)
b) find the intensity level at the same point as part a.(118.51)
c) at what distance would the intensity be one-fourth as much as of that part (a).

i have no problem finding the answer for a and b, but i did have a bit of problem in c. i have tried to answer it which i get r=7.173, but i don't know is it right or wrong. help me for C.

2. Homework Equations c
B=10log(I/Io)
Ia=P/4pie r^2

The Attempt at a Solution


I=p/4pie R^2

i get 7.173 after calculate it.
 
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Check your arithmetic. How much is pi? How much is R? How much is 4 pi R^2?
 

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