Finding combined amplitude of out of phase waves

[novafx]

Homework Statement

"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."

Homework Equations

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

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.

 

[kuruman]

Homework Statement

"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."

Homework Equations

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

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.

Look up the trig identity for sina + sinb.

 

[RoyalCat]

Look up the trig identity for sina + sinb.

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

 

[novafx]

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

 

[RoyalCat]

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

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

 

[novafx]

Ok thanks