# Time difference between two sine waves

by redshift
Tags: difference, sine, time, waves
 P: 53 "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." Should I go about this by assuming... sin(120pi*t) = sin(120pi(t + x) - 20) Any hints appreciated
 Sci Advisor HW Helper P: 2,002 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.
 P: 53 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

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