How far can your voice carry at 40 dB?

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SUMMARY

The discussion centers on determining the minimum sound level required for a person to hear a shout from a distance of 100 meters, concluding that 40 dB is the necessary sound level. The formula used is β = 10log(I/Io), where I represents intensity and Io is the reference intensity. Participants emphasize the importance of understanding sound intensity and distance calculations, particularly using the formula I = P/A = P/4∏r^2. The challenge lies in applying these concepts without a clear baseline for sound perception at that distance.

PREREQUISITES
  • Understanding of sound intensity and decibel levels
  • Familiarity with the formula for sound intensity: I = P/A = P/4∏r^2
  • Knowledge of logarithmic functions in relation to sound measurement
  • Basic principles of sound propagation in open environments
NEXT STEPS
  • Study the relationship between sound intensity and distance using the inverse square law
  • Learn about the human threshold of hearing and its implications for sound perception
  • Explore practical applications of decibel calculations in real-world scenarios
  • Investigate how environmental factors affect sound transmission over distances
USEFUL FOR

Acoustics students, physics enthusiasts, sound engineers, and anyone interested in the principles of sound propagation and measurement.

Kavorka
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You are in a park when you spot your friend 100 m away. At what lowest decibel should you shout your greetings so that your friend can just hear you? Assume that your friend has normal hearing.

My prof never gave an example of how to do this and I can't figure it out. The correct answer is 40 dB. We know that β = 10log(I/Io) and I = P/A = P/4∏r^2

I really just have no idea how to do this because they gave no baseline to compare the 100 m distance to.
 
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It might hinge on a person's ability to just barely discern a change in sound of 1dB. But that still won't get me to a solution.

Maybe try working backwards. If it's 1dB at 100m radius, at what radius is it 40dB?
 

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