Destructive interference Sound question

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A student conducts an experiment with speakers placed 4.0 m apart, generating sound at a consistent frequency. He observes a quiet spot at a location 2.0 m from one speaker and 2.3 m from the other, indicating destructive interference. The path difference (PD) is calculated using the equation PD = (n-1/2) λ, where n represents the nodal line. The discussion focuses on understanding how this quiet spot is formed due to destructive interference and how to determine the frequencies involved. The key takeaway is the relationship between path difference and the resulting sound interference patterns.
zee abadin
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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 speakers 4.0 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


No idea how to solve.
 
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How is a quiet spot generated?

What does your equation mean?
 
PD = path difference, so N would be the nodal line.
I guess quiet spots are generated during points of destructive interference? Am I correct?
 
Yes. So now you need to figure out where this is occurring in the problem.
 
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