# No clue where to start

Hey,

My question:

Two loudspeakers face each other, vibrate in phase, and produce identical 440Hz tones. A listener walks from one speaker toward the other at a constant speed and hears the loudness change (loud-soft-lound) at a frequency of 3.0 Hz. The speed of scound is 343m/s What is the walking speed?

Ok, where do I start?

I can find the wavelength with 440Hz, and speed of sound.
I'm guessing V=d/t? to find the walking speed. Help! :yuck:

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Astronuc
Staff Emeritus
If the two vibrations are in phase, they are adding or reinforcing each other.

What happens when an observer moves toward or away from an acoustic source? Doppler shift.

See, the observer is moving from one speaker to another, so it's moving away from a source to a source. Is the frequency observed 3Hz, or is that the beat frequency?

:uhh: Astronuc..? Still confused here lol.

The doppler effect can't work here?

Doc Al
Mentor
Consider that the sound waves from each speaker will interfere with each other, creating a standing wave pattern. What's the spacing between the anti-nodes? (Hint: anti-nodes occur where the waves constructively interfere. For example, right in the middle between the speakers will be a spot where the waves are in phase.)

hmm, let me see if I can get where you're going. The distance between the two speakers, let's say L. I want to find L do I can see what distance the man will walk, then find velocity, but I need time. Ok, I can find L from L=v/2f?

Doc Al
Mentor
The distance between speakers is irrelevant. Find the distance between the points of constructive interference. (Hint: That distance is related to the wavelength of the sound.)

The spacing between the antindoes? isn't that dependent on the harmonics? if it was the 1st it would lambda/2, if it was the 2nd, then lambda? Wait, that's for nodes, for the 2nd the distance is lambda/2.

Another thing(s): it says (loud-soft-lound), doesn't that mean when loud, we get constructive, soft -destructive. So wouldn't there be a node in the middle? I don't see how finding this will lead to the man's velocity, not yet anyway.

Doc Al
Mentor
NotaPhysicsMan said:
Another thing(s): it says (loud-soft-lound), doesn't that mean when loud, we get constructive, soft -destructive. So wouldn't there be a node in the middle?
Yes. The anti-nodes are separated by nodes.
I don't see how finding this will lead to the man's velocity, not yet anyway.
If you know the distance between anti-nodes (or nodes) and the man's walking speed you can figure out the frequency of loudness changes that he hears. For example: if the anti-nodes were 2 feet apart, and the man walked 2 feet per second, then he'd hear the sound alternate from loud-to soft-to loud every second: 1 Hz.

But we dont' know the man's walking speed. Wait, so let's say that the distance between the antinodes were lambda/2. So to find lambda, lambda=speed of sound/frequency. So 343m/s / 440hz. ok so 0.77m/2 as distance between antinodes is lambda/2. I get 0.40m. He hears loudsoftloud at 3hz which is 0.33s. V=d/t, that would be .40m/0.33s, I get 1.20 m/s?

Doc Al
Mentor
Sounds good to me.

Yes, Thanks!