Very fundamental qn on waves

[Wen]

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?

 

[Galileo]

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.

 

[Wen]

but the answer is 156 degree?

 

[mukundpa]

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