ANS: Perpendicular bisector of the line joining the two points.

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SUMMARY

The discussion centers on the calculation of constructive interference for sound waves emitted from two speakers located at the origin and at (0, 3.00m). The correct distance for constructive interference is determined to be x = 1.50m. The initial attempt incorrectly equated the difference in distances to the wavelength (λ = 2.00m) without considering that constructive interference can also occur at integral multiples of the wavelength. The locus of points equidistant from the two speakers is a perpendicular bisector of the line segment joining them.

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Homework Statement



One speaker is located at the origin and the other is located at (x,y)=(0,3.00m). The speakers emit identical sound waves of wavelength 2.00m which are initially in phase. Where does constructive interference occur?

ANS: x=1.50m

The Attempt at a Solution



Difference of the distance of the two speakers = λ = 2
√(3^2 + d^2) - d = 2
(3^2 + d^2) = (2 + d)^2
9 + d^2 = 4 + 4d + d^2
5 = 4d
d = 1.25m

What's wrong with my attempt, please?
 
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scrubber said:
Difference of the distance of the two speakers = λ = 2
√(3^2 + d^2) - d = 2
(3^2 + d^2) = (2 + d)^2
9 + d^2 = 4 + 4d + d^2
5 = 4d
d = 1.25m

What's wrong with my attempt, please?

What is d ? It is difficult to follow what you have done.

The difference of the distance to a point from the speakers for constructive interference is not necessarily λ .Yes ,it can . But it can also be 0 or any other integral multiple of λ .

What is the locus of a point equidistant from two points ?
 

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