doppler effect question - professor strikes a 440 HZ tuning fork and moves away from you @ 3.0 m/s...?

Question

what beat frequency do you hear if the velocity of sound on that day is 340 M/s

okay. so here's what I got. here's the equation for away right?
fo = fv/(v + va)

so..

440= fv(343)

..but the answer is not coming out correctly. what did I do wrong?

Answer 1

We can use the following equation:

f' = f ([v+/-vo]/[v+/-vs])



where f = frequency of turning fork

where f' = frequency you the observer hears

where v = velocity of sound (340m/s)

where vo = velocity of observer

where vs = velocity of source



Like you said, the fork is moving away so it must be a + vs denominator and since you're not moving, vo = 0, so we get

f' = f (340/[340+3])

f' = (440)(340/343)

f' = 436.1516035



Now, I think you actually forgot to answer the question completely, because you want BEAT FREQUENCY, which is simply

beat frequency = f - f'

= 440- 436.1516035

= 3.84



[Answer: beat frequency is 3.84 Hz]



I can't change my answer cause I'm using the facts you gave me. One problem I see with this question is that it doesn't tell you 100% that the observer isn't moving as well... if the observer IS moving, then a different answer would be produced.

Answer 2

Say normally he would stand next to you so a sound wave coming from the fork at time t reaches you at the same time, at time t. Now since he moves, at time t he has moved the distance d = t*3 m/s from you, so a sound wave released at time t reaches you at time t + d/v = t + t*3 m/s / (340 m/s) = t*(1+3/340) = t*343/340. Since the time it takes is now being multiplied by 343/340, the time between two sound waves, aka the period, is also multiplied with 343/340. Now since the frequency is inverse proportional to the period, the frequency is divided by 343/340, or multiplied by 340/343. So the new frequency is 440*340/343 Hz.

Answer 3

i haven't done this topic, but am trying the straightforward 9possibly wrong approach)



440= 340/ wavelength

therefore wavelength= 0.7727m



moving away from you at 3 therefore effective velocity = 337



f=337/0.7727= 436hertz