Constructive and Destructive Interference

[Calu]

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.

 

[Doc Al]

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.

 

[Calu]

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.

 

[Doc Al]

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.

 

[Calu]

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?

 

[Doc Al]

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.)

 

[Calu]

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.