Interference of sound waves

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Homework Statement


Two in-phase loudspeakers, which emit sound in all directions,
are sitting side by side. One of them is moved sideways by 3.0 m,
then forward by 4.0 m. Afterward, constructive interference is
observed 1/4 and 3/4
of the distance between the speakers along the
line that joins them. What is the maximum possible wavelength
of the sound waves?

Homework Equations


Δr=r2 - r1 =mλ

The Attempt at a Solution


The 2 speakers are separated by 5 m, so one speaker is r1= 1/4 x 5m = 1.25m from the point of constructive interference, another speaker is r2=3/4 x 5m = 3.75m from the point of constructive interference.
Δr=r2 - r1 =mλ
= 3.75m-1.25m=2.50m =mλ
So λ=2.5/m
I got λmax=2.5m when m=1
But the answer is 5meters. I don't know why.
Any help is appreciated!
 

Answers and Replies

  • #2
haruspex
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I don't know why.
Neither do I.
Maybe it's a typo, should be destructive.

On the other hand, not entirely happy with your answer if we take the question literally. It only says the interference is constructive, not that it is maximally constructive. But that still does not yield 5m.
 
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Sorry, I just assumed that constructive interference means the interference is maximally constructive because I only know how to solve questions when the interference is maximally constructive or maximally destructive.
I am not surprised that the answer is wrong because the textbook has lots of errors.
Thank you for confirming what I did is correct though :)
 
  • #4
haruspex
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Sorry, I just assumed that constructive interference means the interference is maximally constructive because I only know how to solve questions when the interference is maximally constructive or maximally destructive.
I am not surprised that the answer is wrong because the textbook has lots of errors.
Thank you for confirming what I did is correct though :)
I feel sure they meant maximally con-/de-structive. In fact, if we admit partially constructive the answer to the question is unbounded. For partially destructive, anything just under 10m, I think.
 

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