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

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The discussion focuses on calculating the phase difference between two sinusoidal waves defined as y1=2sin(20x-32t) and y2=2sin(25x-40t) at the point x=5 and t=2s. The calculations show that y1 equals 2sin(36) and y2 equals 2sin(45), resulting in a phase difference of 9 radians, which converts to approximately 515.66 degrees. The general formula for phase difference at any point x is derived as (25x-40t)-(20x-32t)=5x-8t. The importance of using proper units is emphasized, as the phase difference should be expressed in radians. The final phase difference is clarified to be 156 degrees after accounting for the conversion.
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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