If you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left, will the sound that you hear be louder than the sound you would hear if only one speaker were in use?

Complete Question:

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.

If you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left, will the sound that you hear be louder than the sound you would hear if only one speaker were in use?

Answer:

Yes.

Explanation:

In order to have a constructive interference between two waves of the same frequency, there must be a path difference of even multiples of the half wavelength, as follows:

Δd = (2*n) * λ/2

There is a fixed relationship between frequency, wavelength and propagation speed in any wave, as follows:

v = λ*f

Solving for λ, based in the information that we have of frequency and the speed of sound, we have:

λ = v/f = 344 m/sec / 688 1/sec = 0.5 m

So, the speaker A is at a distance (measured in λ) of 6 units, and speaker B is at 7 units, so the difference is just one wavelength, which means that the information is arriving (from both sources) in phase.

This translates in a louder sound than if only one speaker were in use.