Calculating Frequencies of Speakers using Interference Patterns

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SUMMARY

The discussion centers on calculating the frequencies of sound produced by two speakers placed 4.0 meters apart, with a sound speed of 350 m/s. The student identifies a quiet spot at a distance of 2.0 m from one speaker and 2.3 m from the other, indicating a phase difference. The relevant equation for this problem is PD = (n-1/2) λ, which relates the path difference (PD) to the wavelength (λ) and the harmonic number (n). The student attempts to derive the frequency using the formula f = v/λ, but seeks clarification on the calculations involving the distances.

PREREQUISITES
  • Understanding of wave mechanics and sound propagation
  • Familiarity with the concept of path difference in wave interference
  • Knowledge of the relationship between frequency, wavelength, and wave speed
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of wave interference and standing waves
  • Learn about calculating wavelength from frequency and speed of sound
  • Explore the concept of phase difference in sound waves
  • Investigate practical applications of sound wave interference in acoustics
USEFUL FOR

Students in physics, acoustics engineers, and anyone interested in sound wave behavior and interference patterns.

Hannahj1
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Homework Statement


A student enters Best Buy prepared to buy a pair of speakers. Before he does so, he conducts an experiment with them. He places the speakers4.0 m apart and connects a signal generator to both speakers that produces a single and consistent tone. (constant wavelength and frequency) He then walks to a point that is 2.0 m from one speaker and 2.3 m from the other. At that point he notices a quiet “spot”. If the speed of the sound in the room is known to be 350 m/s, calculate the possible frequencies being played by the speakers.

Homework Equations


PD = (n-1/2) λ

The Attempt at a Solution


f = v/(lambda) = 350/6(2n + 1). Am i on the right track? I don't really understand how the 2m and 2.3 m is involved in this question.
 
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Hello,

Well, what does the PD in your relevant equation stand for ?

By the way, I don't really understand the step from there to 350/6(2n + 1), so if yuo could explain what you are doing a little bit ?
 

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