Calculating Beat Frequency in the Doppler Effect

[lha08]

Homework Statement

A boy is walking away from a wall towards an observer at a speed of 1 m/s and blows a whistle whose frequency is 680 Hz. THe number of beats heard by the observer is ____.
(Velocity of sound in air=340 m/s)
a) zero
b)2
c)8
d)4

Homework Equations

The Attempt at a Solution

For this question, I used f(observer)=f(source)v/(v-v(source)). In this case, when i plugged in the number i got 682 Hz...but the only thing i can think of is to subtract 682 from 680 Hz which gives 2...i don't know why if it's right though...

 

[rl.bhat]

Observer hears two sounds, one directly from the boy who is moving with 1 m/s and another reflected from the wall which appears to be moving with 2 m/s.

 

[lha08]

Observer hears two sounds, one directly from the boy who is moving with 1 m/s and another reflected from the wall which appears to be moving with 2 m/s.

how did you get 2 m/s?

 

[rl.bhat]

If a person in front of a mirror moves towards you with a velocity 1 m/s, the image appears to be moving with 1 m/s with respect to the mirror away from you. And with respect to the person the image appears to be moving 2 m/s away from you. Same thing happens here.

 

[lha08]

If a person in front of a mirror moves towards you with a velocity 1 m/s, the image appears to be moving with 1 m/s with respect to the mirror away from you. And with respect to the person the image appears to be moving 2 m/s away from you. Same thing happens here.

So in every problem that's like this, when sound waves bounce off a wall, it will arrive to the observer at double the velocity?

 

[rl.bhat]

So in every problem that's like this, when sound waves bounce off a wall, it will arrive to the observer at double the velocity?

Velocity of the sound does not change. If the source is moving towards you with velocity v, the image of the source moves away from you with velocity 2v.

 

[lha08]

Velocity of the sound does not change. If the source is moving towards you with velocity v, the image of the source moves away from you with velocity 2v.

what do you mean by "image of the source"?

 

[rl.bhat]

You will be receiving two sounds. One directly from the boy and other reflected from the wall which can be taken as from the image of boy in the wall.

 

[ImAnEngineer]

Observer hears two sounds, one directly from the boy who is moving with 1 m/s and another reflected from the wall which appears to be moving with 2 m/s.

Huh? The wall is moving with 2m/s ? ... Your explanation is a bit unclear with the mirrors and so on.
So what is moving how fast with respect to what? And how is that useful?

I think it might be zero if there is destructive interference, I don't see how you could get 2, 4 or 8. I have no idea how to prove this though.

 

[Dweirdo]

the velocity of the sound is independent of the source velocity...for an observer in rest relative to the air or any other medium.
well having no idea what "beats" mean I can't really help, but the note at the begging of the post should help.
and the velocity of the sound "bouncing" from the wall will be 340 m/s as well.
hope that helps in any way.

 

[Doc Al]

Observer hears two sounds, one directly from the boy who is moving with 1 m/s and another reflected from the wall which appears to be moving with 2 m/s.

Velocity of the sound does not change. If the source is moving towards you with velocity v, the image of the source moves away from you with velocity 2v.

Why do you think that the image of the source moves away with twice the velocity? The image appears to be moving away at 1 m/s. (The wall is not moving.)

There are two sounds heard:

(1) The direct sound, the source of which approaches the observer at 1 m/s. Find that frequency using the Doppler formula.

(2) The reflected sound. The wall just reflects the same frequency that it receives. From the wall's point of view, the source moves away at 1 m/s. Find that frequency using the Doppler formula. (Since the wall is stationary, there is no second Doppler effect to worry about.)

You can also view the reflected sound as being produced by the reflected image, which moves away at 1 m/s. Same answer, of course.

 

[rl.bhat]

Thank you Doc Al