Finding the Walking Speed: Solving for Velocity with 440Hz and Speed of Sound

[NotaPhysicsMan]

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!

 

[Astronuc]

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.

 

[NotaPhysicsMan]

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?

 

[NotaPhysicsMan]

Astronuc..? Still confused here lol.

 

[NotaPhysicsMan]

The doppler effect can't work here?

 

[Doc Al]

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.)

 

[NotaPhysicsMan]

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]

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.)

 

[NotaPhysicsMan]

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.

 

[NotaPhysicsMan]

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]

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.

 

[NotaPhysicsMan]

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]

Sounds good to me.

 

[NotaPhysicsMan]

Yes, Thanks!