Destructive Interference

[Gentec]

Good day - I would appreciate some direction. I have done the problem a few different ways and end up with different answers each time - which seems to be reasonable answers to all.

Two speakers are 3.2 m apart and facing the same directions are in phase. They each produce 214 Hz tone. What is the shortest distance directly in front of one speaker where there would be destructive interference?. Take sof sound 343 m/s.

Am i right to treat m =0 seeing it is in phase?

Thank you very much for your time.

 

[Astronuc]

What do you mean m=0?

It seems the speakers are 3.2 meters (m) apart.

Have you calculated the wavelength of the sound, and compared it to the separation? Remember the speakers are in phase.

Complete destructive interference is the distance where the peak of one cancels with the trough of the other.

Try to determine the distance to the first trough in front of one of the speakers.

 

[Gentec]

Thanks for getting back to me.
I have worked out the lamda to be 1.6 m. Do I need to set up the right equations to have them going opposite directions and see where they sum to zero?

 

[ComputerGeek]

if a wave length is 1.6 meters, then since a wave length is half the distance to the other speaker the cancelation point should be?

 

[Gentec]

I would say 1.6 m but would that be all there is to the question though.

 

[HallsofIvy]

Find the first point (there will be an infinite number of them) such that the difference between the distance from that point to each speaker is exactly half a wavelength.

Set up a coordinate system so that one of the speakers is at (0,0) and the other is at (3.2,0). Assuming that you are directly in front of the first speaker, your position is (0,y) so your distance from that speaker is y and your distance from the other speaker is sqrt(3.2²+ y²). Find y so that
sqrt(3.2²+ y²)-y= 0.8.

Apparently you did not understand what ComputerGeek said.

 

[Gentec]

Thanks for the clarification. Appreciated