time difference between two sine waves

by redshift
Tags: difference, sine, time, waves
redshift is offline
Nov20-04, 07:15 AM
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
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Galileo is offline
Nov20-04, 08:04 AM
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P: 2,004
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:
[tex]A\sin(kx-\omega t + \phi)[/tex]

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:

[tex]A\sin(-\omega t + \phi)=A[/tex]
Where [itex]\phi[/itex] is 20 degrees expressed in radians.
redshift is offline
Nov20-04, 08:34 AM
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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