Speakers in a field/ destructive interferece

[ravenprp]

Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.

You are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left

What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? D=
-----------

Ok, I've setup a picture that looks something like this

Speaker A ------- 3.0m --------- Me --------- 3.5 m ----- Speaker B


Ok, now... I know that I can get perfect destructive interefrence when the path length difference is HALF integer number wavelengths

so, v = lambda * f = 343 m/s = lambda * 688hz ... lambda =~ .500 m

so, lamda/2 = .250 m ... That is the shortest distance I know I have to travel in order to have perfect destructive interference.. but I don't know *how/where to* travel to with this distance

Now I'm cluless as to what I have to do?

 

[ravenprp]

anybody have any idea?

 

[kyle8921]

To find the exact spot where you will experience perfect destructive interference, you need to use the formula for path length difference:

Δd = |d2 - d1|

where Δd is the path length difference, d2 is the distance from speaker B to your new position, and d1 is the distance from speaker A to your new position.

In this case, we know that the path length difference for perfect destructive interference is λ/2, which is approximately 0.250 m. So, we can set up the equation:

0.250 m = |3.50 m - d1| - |3.00 m - d1|

Solving for d1, we get:

d1 = 2.75 m

So, the shortest distance you need to walk forward is approximately 2.75 m to experience perfect destructive interference and not hear the speakers.