# Time difference between two sine waves

1. Nov 20, 2004

### redshift

"There are two sine waves having a phase difference of 20 degrees. After one reaches its maximum value, how much time will pass until the other reaches its maximum, assuming a frequency of 60 Hz."

sin(120pi*t) = sin(120pi(t + x) - 20)

Any hints appreciated

2. Nov 20, 2004

### Galileo

You have two sines which have are functions of position and time. (actually, considering them function of time alone is sufficient)
They both have the form:
$$A\sin(kx-\omega t + \phi)$$

Assume the first wave reaches its maximum A at time t=0 and position x=0.
Then you have to find t when the second wave reaches its max A:

$$A\sin(-\omega t + \phi)=A$$
Where $\phi$ is 20 degrees expressed in radians.

Last edited: Nov 20, 2004
3. Nov 20, 2004

### redshift

I get it. Since 20 degrees = pi/9, moving LHS A to RHS gives
sin (-120pi*t + pi/9) = 1
so, -120pi*t + pi/9 = pi/2
and finally t = 7/2160 seconds

Many thanks