Destructive intereference in a wave

[Terp]

Homework Statement

Homework Equations

None really.

The Attempt at a Solution

I know that to make a wave completely destructive to the original I'd have to add pi, so I tried the answer 0+pi*n, which was wrong. I also tried 0 + 3pi*n, which would shift the wave to another destructive position but that wasn't correct either. Would any of you guys know what I'm doing wrong or overlooking? Thanks a lot!

I'm thinking that it may be pi + 2*pi*n, but I want to get some opinions before I try submitting.

 

[Terp]

Bump!

 

[Moetasim]

Hello,

Destructive interference occurs when two waves meet and their amplitudes cancel each other out, resulting in a wave with a lower amplitude. In order to completely cancel out the original wave, the two waves must have opposite phases (i.e. one is at a peak while the other is at a trough). This can be achieved by adding pi (180 degrees) to the phase of one of the waves.

In your attempt, you are correct in adding pi to the phase, but you also need to consider the initial phase of the original wave. If the original wave has an initial phase of 0, then adding pi would result in a phase of pi. However, if the original wave has an initial phase of pi/2, then adding pi would result in a phase of 3pi/2.

In general, the phase difference between the two waves should be an odd multiple of pi. So the correct answer would be 0 + (2n+1)*pi, where n is an integer.

I hope this helps! Good luck with your submission.