How Do You Combine Two Sound Waves Mathematically?

[mgoddard]

Hi, I need to determine the sum of the two sound waves and express it in the form y=Csin(kx-wt-"theta") where w is omega. The two waves are

y=Asin(kx-wt) where w is omega
y=Bsin(kx-wt-"phi") where w is omega

I used a trigometric formula and got it to the point where it equals

y=Asin(kx-wt)+B[sin(kx-wt)cos(phi)-cos(kx-wt)sin(phi)] and I have simplified a little but I cannot get it into the form stated above where y=Csin(kx-wt-theta) Any suggestions?

As well the question states C depends on A,B and phi, and Theta depends on A, B, and phi as well.

Thanks for your time
M Goddard

 

[Galileo]

Hint: Use complex numbers