How Close to Speaker B Must You Be for Destructive Interference at 172 Hz?

[sreya]

Homework Statement

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 Hz. You are 8.00 m from speaker A. Take the speed of sound in air to be 344 m/s.

What is the closest you can be to speaker B and be at a point of destructive interference?
Express your answer in meters.

Homework Equations

$f = \frac{v}{\lambda}$
$\frac{\Delta L}{\lambda} = .5,1.5,2.5,...$

The Attempt at a Solution

$\lambda = 344/172 = 2$

$1/2 = .5 => Ans:$1m

The odd thing is that it tells you the distance you are from A but wants to know how close you can get to B but you don't know the distance between the two.

The answer is 1, since that would give you 1/2 = .5 but that seems like to me that you're 1m away from A, since we don't know how close we are to B

 

[TSny]

It might help to use more explicit notation for the various distances. Let $d_A$ be your distance from speaker A and $d_B$ your distance from speaker B. You are given $d_A = 8$m, but let's keep using the symbol $d_A$. We can plug in numbers later.

You wrote $\frac{\Delta L}{\lambda} = .5, 1.5, 2.5, ...$.

You can write this as $\frac{\Delta L}{\lambda} = (n+\frac{1}{2})$ where $n = 0, 1, 2, ...$.

Can you express this equation in terms of the symbols $d_A$ and $d_B$?