AAMC 10 Question on Destructive Interference

[rls303]

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Hi,
I had a question regarding Item 35, when you have destructive interference, I thought that the phase difference is always multiples of pi/2, so should it not be 90 degrees instead of 180 degrees?

I don't understand.

Thanks in advance🙂

 

[lorenzomicron]

Hi,
I had a question regarding Item 35, when you have destructive interference, I thought that the phase difference is always multiples of pi/2, so should it not be 90 degrees instead of 180 degrees?

I don't understand.

Thanks in advance🙂

Nope. total destructive interference is where the phase difference is 180 degrees, which is pi.

 

[rls303]

Nope. total constructive interference is where the phase difference is 180 degrees, which is pi.

Hi, but since we are looking for destructive interference, shouldn't it be pi/2....man I just took Physics 3C last quarter and I thought I had this down! 🙁

 

[lorenzomicron]

oh yeah, that was a typo. sorry, yeah. so pi/2 is 90 degrees. pi is 180 degrees, and 2*pi is 360 degrees.

if phase difference is 2*pi, the waves overlap exactly at the same points, leading to constructive interference (assume: same frequency sinusoidal/periodic waves).

if the waves are pi/2, then it's just half-translated onto itself; this is partially destructive/partially constructive.

however, if the waves are pi phase different, then they are are opposite; this leads to fully destructive interference.

however, this is the Phase Difference, absolute. there are some formulations of the phase difference which use different pi:

destructive if P=pi*n, where n=1, 3, 5, 7, ....
P=pi/2*n, where n= 2, 4, 6, 8, ....

the difference between adjacent waves are still pi