Constructive Interference from Speakers on an x-axis

[ab200]

Homework Statement

Two speakers, A and B, are at the same point on an x-axis and each emits sound with a wavelength of 0.25 m. Speaker B's phase constant is 260 degrees larger than speaker A's phase constant and each produces an amplitude of 10 Pa.

What is the minimum distance you can move speaker A to achieve constructive interference along the x-axis? Give a positive answer regardless of direction, in m.

Relevant Equations

ΔΦ/2π = Δx/λ + ΔΦo/2π = m , m = 0,1,2,3...

The first part of this question asks for the maximum amplitude produced, which I found to be 12.86 Pa. I was able to set up the expression for the combined wave equations.

However, I am struggling to understand how to set up and solve an expression to find the distance I could move one of the speakers. I have wavelength, frequency, and amplitude, as well as difference in phase constant. Am I solving for phase difference?

 

[haruspex]

Am I solving for phase difference?

It's not entirely clear what you mean by that. Please post an attempt based on that approach. An attempt is required by forum rules anyway, and it will clarify what you have in mind.

 

[ab200]

It's not entirely clear what you mean by that. Please post an attempt based on that approach. An attempt is required by forum rules anyway, and it will clarify what you have in mind.

I apologize — after working on it again I arrived at the correct answer. I’m not entirely sure what I did the first time, but I suspect I didn’t convert degrees into radians when calculating difference in initial phase.