Posted by **sarah** on Wednesday, November 10, 2010 at 9:02am.

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 \rm Hz. You are 8.00 \rm m from speaker A. Take the speed of sound in air to be 344 \rm m/s.

What is the closest you can be to speaker B and be at a point of destructive interference?

- physics -
**bobpursley**, Wednesday, November 10, 2010 at 9:13am
draw the figure. draw a triangle short side from A, long side from B, other side A to B.

so the difference between the short side and the long side has to be an even multiple of 1/2 wavelength.

start with the wave equation

lambda= v/f

so long side-short side= n(v/2f)

do the degenerate triangle first, where short+long= AB (a point on AB)

nv/2f+nv/2f+v/2f=ab

or v/2f(2n+1)=ab

you know ab as 8m, so solve for n

then solve for short side length.

Now do the same thinking for some triangle .

Use the law of cosines to find short side, then minimize it with differential calculus.

You will find the answer, and discovering something magic about the angle from B, it gets minimized also.

## Answer this Question

## Related Questions

physics - A student sets up two speakers spaced 2.5 meters apart, each playing ...

Physics - Imagine you are in an open field where two loudspeakers are set up and...

Two Loudspeakers in a open field Pjysics - Imagine you are in an open field ...

physics help - Imagine you are in an open field where two loudspeakers are set ...

physics - Two loudspeakers in a 20°C room emit 629 Hz sound waves along the x-...

physics - Which of the following conditions is not necessary to observe an ...

physics - waves - Two sinusoidal waves, identical except for phase, travel in ...

physic - The waves emitted from a source A is given by y1 = 6 sin π(20t – 0...

physics - Two waves traveling on a string in the same direction both have a ...

physics - Two waves traveling on a string in the same direction both have a ...