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

[scrubber]

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?

 

[Tanya Sharma]

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 ?