Destructive intereference in a wave

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In summary, destructive interference in a wave occurs when two waves of equal amplitude and opposite phase meet, resulting in a smaller or even zero amplitude wave. This can happen in all types of waves and can be seen in real-world examples such as noise-canceling headphones and ocean waves. Destructive interference is different from constructive interference, which results in an increase in amplitude when two waves of equal amplitude and phase meet.
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Terp
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Homework Statement



wtf.jpg

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.
 
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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.
 

1. What is destructive interference in a wave?

Destructive interference in a wave occurs when two waves of equal amplitude and opposite phase meet. This results in the waves canceling each other out, creating a smaller or even zero amplitude wave.

2. How does destructive interference affect the amplitude of a wave?

As mentioned, destructive interference causes the amplitude of a wave to decrease or even become zero. This is because the two waves are essentially canceling each other out, resulting in a smaller or no amplitude at all.

3. Can destructive interference occur in all types of waves?

Yes, destructive interference can occur in all types of waves, including sound waves, light waves, and water waves. Any two waves with the same frequency and opposite phase can experience destructive interference.

4. What are some real-world examples of destructive interference in waves?

One example of destructive interference is noise-canceling headphones. These headphones produce a sound wave with the opposite phase of the ambient noise, resulting in destructive interference and canceling out the noise. Another example is when two ocean waves meet and cancel each other out, creating a calm spot in the water.

5. How is destructive interference different from constructive interference?

While destructive interference results in a decrease or cancellation of amplitude, constructive interference results in an increase in amplitude. This occurs when two waves of equal amplitude and phase meet, creating a larger wave with a higher amplitude.

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