Solving the Volume Increase: Finding L with Two Speakers

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SUMMARY

The problem involves determining the distances at which an observer hears an increase in volume from two speakers emitting a 343 Hz sound. The speed of sound is given as 343 m/s, resulting in a wavelength of 1 meter. The correct distances for the second speaker, positioned at distance L from the first, are multiples of the wavelength: 0 m, 1 m, 2 m, and 3 m. This phenomenon occurs due to constructive interference when the speakers are in phase.

PREREQUISITES
  • Understanding of sound wave properties, specifically frequency and wavelength.
  • Knowledge of constructive interference in wave physics.
  • Familiarity with basic trigonometry for visualizing wave interactions.
  • Ability to interpret sound wave diagrams and phase relationships.
NEXT STEPS
  • Study the principles of wave interference, focusing on constructive and destructive interference.
  • Learn about sound wave properties, including frequency, wavelength, and amplitude.
  • Explore practical applications of sound waves in acoustics and audio engineering.
  • Investigate the effects of distance on sound intensity and volume perception.
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Physics students, audio engineers, and anyone interested in understanding sound wave behavior and interference patterns.

nemzy
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I got this wrong on a midterm, i have NO IDea absolutely how to solve this type of problem. I asked my TA too and he has no idea

-An observer hears the 343 Hz sound produced by two speakers. One is 5m from him, the other is at a distance L the first and can be moved. Taking the speed of sound to be v=343 m/s, for what values of L will the observer hear an increase in volume? (assume the speaker can only move to the right of the fixed one and that the amplitude of the waves does not decrease with distance)

the right answer is 0, 1m, 2m, 3m...

anyone have any idea why?

thanks
 
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The speed of sound is 343 m/s, so the wavelength at 343 Hz is 1 m. So 2 in-phase speakers will reinforce the signal at distances of n times 1 m apart. If you still don't get it, draw yourself a picture. P.S. Get another TA.
 

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