# Homework Help: Two in-phase loudspeakers on a coordinate plane

1. Sep 15, 2009

### tiger1

1. The problem statement, all variables and given/known data
Two in-phase loudspeakers are located at (x, y) coordinates (-3.0, +2.0) and (-3.0, -2.0) . They emit identical sound waves with a 2.0 m wavelength and amplitude a.

Determine the amplitude of the sound at the five positions on the y-axis (x=0):
with y=0.0
with y=0.5
with y=1.0
with y=1.5
with y=2.0

2. Relevant equations
k=2pi/wavelength
D(x,t)=A(x)cos(wt)
phase change = [2pi(path-length difference)]/(wavelength) + (initial phase change)

Don't know what other equations I need

3. The attempt at a solution
I could find the phase change, but I can't see how that will relate to the amplitude because I don't have the angular frequency or displacement.

Variables I can find: path-length difference, wavelength, k, phase change

2. Sep 15, 2009

### tiny-tim

Welcome to PF!

Hi tiger1! Welcome to PF!

(have a pi: π and an omega: ω )
You do have the angular frequency … it's ω.

using the usual trignometric identities, you can show that the sum of Acos(ωt + θ) to Acos(ωt + φ) is of the form Bcos(ωt + ψ).

3. Sep 15, 2009

### tiger1

Figured it out using A=|2a cos[1/2(change in phi)]|

Last edited: Sep 15, 2009