Two loudspeakers, finding amplitude.

[hydrocodone]

Homework Statement

Two in-phase loudspeakers emit identical 1000 Hz sound waves along the x-axis. What distance should one speaker be placed behind the other for the sound to have an amplitude 1.60 times that of each speaker alone?

Homework Equations

None given, but I assume:
v=f$$\lambda$$
A = 2asin(kx)

The Attempt at a Solution

1.6a = 2asin(kx)

Found k=(2pi)/wavelength = (2pi/0.343)
using v = 343 m/s

arcsin(0.8)=18.318x

x = 0.0506m

But this answer is wrong. Help?

 

[rl.bhat]

You have to add the amplitudes as vectors.
(1.6*a)^2 = a^2 + a^2 + 2*a*a*cos(phi) where phi is the phase difference = 2*pi*x/wavelength

 

[hydrocodone]

Thanks!