Constructive and Destructive Interference

AI Thread Summary
The discussion revolves around determining whether sound waves from two speakers are in constructive or destructive interference based on their distances from a listener. The listener is positioned 5m back and 2m to the side of the speakers, which are 2m apart, emitting sound at 700Hz. Key calculations involve finding the correct distances from each speaker and the wavelength of the sound, which is calculated to be approximately 0.487m. The difference in distances from the listener to each speaker is crucial for determining the type of interference, with a difference of about 0.446m suggesting constructive interference. The conclusion indicates that the waves are indeed close to a full wavelength difference, resulting in constructive interference.
Calu
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Homework Statement



Two speakers are 2m apart. You stand 5m back from the centre of the two speakers, and 2m to the side. The speakers are emitting sound at 700Hz, take the speed of sound to be 341 m/s.

Are the waves in constructive or destructive super position?

Homework Equations




The Attempt at a Solution



I'm really stuck on this question. I'm not even sure of any relevant equations that I can use. I think I'm √29m from the centre; √26m from one speaker and 6m from the other. If that helps at all.

Thank you for any help in advance.
 
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The distance you are from the speakers is key, actually the difference in the distances. If they were the same distance from you, then things would be in phase. If they are half a wavelength different, they would be out of phase.

First get the distances right. √26 m makes sense for one, but not 6 m.

Once you get the distances correct, figure out the wavelength and compare.
 
I keep getting 6m for the second speaker. Taking the first to be the one on the left, I move 1m right to be in the centre, then 5m vertically, followed by 2m left. This gives me a 5m x 1m triangle, and √26m for the distance. I then take the right speaker move 1m left, 5m vertically, and 2m left again. Should this not give me a 5m x 3m triangle and √36m distance?

I also get a wavelength of 0.487m.
 
Calu said:
Should this not give me a 5m x 3m triangle and √36m distance?
52 + 32 ≠ 36

I also get a wavelength of 0.487m.
Good.
 
Doc Al said:
52 + 32 ≠ 36


Good.

Yep thanks, I was being an idiot.

√34-√29= 0.446m (3.s.f)

Can I say the waves interfere constructively?
 
Calu said:
Yep thanks, I was being an idiot.

√34-√29= 0.446m (3.s.f)

Can I say the waves interfere constructively?
It's close to a full wavelength difference, so it's close to constructive interference. (Looks like they chose the numbers a bit sloppily.)
 
Doc Al said:
It's close to a full wavelength difference, so it's close to constructive interference. (Looks like they chose the numbers a bit sloppily.)

Thank you very much for all your help.
 

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