# Finding combined amplitude of out of phase waves

1. Aug 2, 2009

### novafx

1. The problem statement, all variables and given/known data

"Two waves are traveling in the same direction along a stretched string. The waves are 30.0° out of phase. Each wave has an amplitude of 4.00 cm. Find the amplitude of the resultant wave."

2. Relevant equations

y(x,t) = Asin(kx - $$\omega$$t)

3. The attempt at a solution

Assuming that both waves are sinusoidal, I'm just summing up the two waves as follows:

(4.00 cm)sin(kx-$$\omega$$t) + (4.00 cm)sin(kx-$$\omega$$t + 30)

but I'm not sure how to find a numerical amplitude with this. Thanks for the help.

2. Aug 2, 2009

### kuruman

Look up the trig identity for sina + sinb.

3. Aug 2, 2009

### RoyalCat

And don't forget to use radians to measure the angle, just to make things a bit more consistent.

Last edited: Aug 2, 2009
4. Aug 2, 2009

### novafx

So what do I do with the variables "kx-$$\omega$$t"? They're not given in the problem.

5. Aug 2, 2009

### RoyalCat

You are only asked about the amplitude of the resultant wave. The rest is irrelevant.

6. Aug 2, 2009

Ok thanks