How Do You Calculate the Phase Difference Between Two Sinusoidal Waves?

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Homework Help Overview

The discussion revolves around calculating the phase difference between two sinusoidal waves defined by their equations. The original poster presents the equations and specific values for position and time, seeking to understand the phase relationship between the two waves.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of phase difference using the arguments of the sinusoidal functions at given values of x and t. There is a question regarding whether the waves are in phase and a discrepancy noted in the expected answer.

Discussion Status

Some participants have provided calculations for the phase difference and raised questions about the correctness of the units used. There is an ongoing examination of the implications of these calculations, with no clear consensus reached on the correct phase difference.

Contextual Notes

Participants are discussing the importance of using proper units for phase difference, indicating a potential misunderstanding regarding radians and degrees in the context of the problem.

Wen
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2 sinusiodal waves are defined

y1=2sin(20x-32t)
y2=2sin(25x-40t)

what is the phase difference between this two waves at point x=5 and t=2s. all length in cm.

I sketch the graph y/x and y/t and both have their max amplitude at x=3.2 , and t=3.125s.

so what is the different in phase? Arn't them in phase?
 
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The phase is simply the argument of the sinusoid wave. For y1 and y2 at x=5 and t=2 you get: y1=2sin(36) and y2=2sin(45). So the phase differerence is 45-36=9.

More generally, their phase difference at a certain point x is (25x-40t)-(20x-32t)=5x-8t.
 
but the answer is 156 degree?
 
Taht's why one should always use Proper units. The phase difference is in radiuns.
9 radiuns = 9*180/pi = 515.66 deg. = (360 + 155.66) deg
 

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