Sound wave Interference from Two Speakers

aatari

Hi guys I am having trouble determining a quite spot based on where you stand in respect to distance from the speakers. I have solved the question below but I need someone to explain to me how the "n" value can be used to determine a quite or not-quite spot. Am I looking for whole numbers? If n is a whole number its constructive interference and therefore, noisy spot and if n is not a whole number then its destructive interference and a quite spot?

1. Homework Statement
A student enters Best Buy prepared to buy a pair of speakers. Before he does, he conducts an experiment with them. He places them 4.0 m apart and then connects a signal generator to both speakers that produces a single tone of 240 Hz. He then walks in front of the speakers so that he is 2.0 m from one speaker and 5.0 m from the other. If the speed of the sound in the room is 360 m/s, will he be standing in a “quiet” spot? Explain.

2. Homework Equations
v = f. λ
PD = (n-1/2) λ

3. The Attempt at a Solution

λ = 360/240
λ = 1.5 m

PD = (n-1/2) λ
|5.0 – 2.0| = (n – 0.5) 1.5
3.0 = 1.5n – 0.75
3.0 + 0.75 = 1.5n
3.75 = 1.5n
n = 3.75/1.5
n = 2.5

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TSny

Homework Helper
Gold Member
I would recommend that you approach this more conceptually. You have found the wavelength. How does the path difference compare to λ?

aatari

I would recommend that you approach this more conceptually. You have found the wavelength. How does the path difference compare to λ?
It double the size of the wavelength. So its constructive interference and the person will not be standing at a quite spot.

TSny

Homework Helper
Gold Member
Yes, I think that's all there is to it. (quite → quiet)

• aatari

"Sound wave Interference from Two Speakers"

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