Beat frequency and Doppler shift

[dawn-]

Homework Statement

Angharad stands midway between two speakers with frequencies 258 Hz and 262 Hz. The speed of sound in the air is 340 m/s. If Angharad does not want to hear beats, how fast and in which direction should she run so that the frequencies she hears from the two speakers are the same? What is this frequency she hears?

Relevant Equations

λ=vT
|f1-f2|= fb
(f1+f2)/2 = fc
(v±vo / v±vs)(f) = fo
where v = speed of wave, vo = speed of observer, vs = speed of source, f = frequency of wave, fo = frequency observed

I found the beat frequency to be 4 Hz and the carrier frequency to be 260 Hz, but I'm not sure how to apply them to the solution/integrate the doppler and beat frequency equations?

 

[haruspex]

I found the beat frequency to be 4 Hz and the carrier frequency to be 260 Hz, but I'm not sure how to apply them to the solution/integrate the doppler and beat frequency equations?

Seems to me there are infinitely many solutions if able to run in any direction, so assume it is directly towards one speaker. If the running speed is v and the speed of sound is c, what two frequencies will be heard?

 

[dawn-]

Seems to me there are infinitely many solutions if able to run in any direction, so assume it is directly towards one speaker. If the running speed is v and the speed of sound is c, what two frequencies will be heard?

I'm still real lost... I first thought "hearing no beat" means I should set the beat frequency to zero because f1 needs to equal f2 for that to be true, but that doesn't make any sense if I use that to try and solve for running speed..? What conditions need to be met in order to hear no beat?

 

[haruspex]

hearing no beat" means I should set the beat frequency to zero because f1 needs to equal f2 for that to be true, but that doesn't make any sense if I use that to try and solve for running speed..

Why doesn't it make sense? Anyway, please put that aside for the moment and try to answer the question I asked in post #2.

What conditions need to be met in order to hear no beat?

You are told that:
"so that the frequencies she hears from the two speakers are the same"