What is the frequency (in Hz) of the tone being emitted? (Assume air temperature to be 20°C.)

Question

A person stands directly in front of two speakers that are emitting the same pure tone. The person then moves to one side until no sound is heard. At that point, the person is 7.15 m from one of the speakers and 7.17 m from the other. What is the frequency (in Hz) of the tone being emitted? (Assume air temperature to be 20°C.)

Answer 1

Hi Emma L.,

You should be able to visualize the geometry here?

For the initial condition, the waves arrive (we assume) in phase, so the sound is loudest.

For the final condition, the difference in path length is __ (you calculate!)

That difference must equal exactly (1/2) a wavelength of the particular sound, since the waves arrive exactly out-ouf-phase by 180 degrees and there is silence. So double the value just above to get 1 wavelength.

You can look up the applicable speed of sound.

frequency (s^-1) = speed (m/s) / wavelength (m) . Do you see how the units shake out there (="dimensional analysis")? So you can always 'figure out' the relationship you need among the wave-motion-related variables.

So do the math!

-- Cheers, --Mr. d.