Time difference between two sine waves

In summary, the conversation discusses two sine waves with a phase difference of 20 degrees and a frequency of 60 Hz. The task is to determine the time it takes for one wave to reach its maximum value after the other has already reached its maximum. This can be solved by setting the equations of the waves equal to each other and solving for time, assuming the first wave reaches its maximum at time t=0 and position x=0. The resulting time is approximately 7/2160 seconds.
  • #1
redshift
53
0
"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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  • #2
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.
 
Last edited:
  • #3
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
 

What is the definition of time difference between two sine waves?

The time difference between two sine waves is the amount of time it takes for one wave to complete a full cycle while the other wave is still in the middle of its cycle. This can also be referred to as the phase difference between the two waves.

How is time difference between two sine waves calculated?

The time difference between two sine waves can be calculated by finding the difference between the two waves' phase angles. This is usually measured in radians or degrees and can be calculated using trigonometric functions such as sine, cosine, and tangent.

What factors can affect the time difference between two sine waves?

The time difference between two sine waves can be affected by various factors, including the frequency, amplitude, and phase of the waves. Additionally, any external influences such as noise or interference can also impact the time difference.

Why is time difference between two sine waves important in scientific research?

The time difference between two sine waves is important in scientific research because it can provide valuable insights into the behavior of waves and their interactions. It is also a crucial factor in understanding and analyzing various physical phenomena, such as sound, light, and electromagnetic waves.

How can time difference between two sine waves be measured in experiments?

The time difference between two sine waves can be measured using various methods, such as oscilloscopes, phase meters, and frequency counters. These instruments can accurately measure the phase angles of the waves and calculate the time difference between them.

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