Doppler effect and beat frequency

[Kolika28]

Summary:: Two speakers A and B are at rest, and a listener L stays on the line that connects the two speakers (see picture). The speakers have almost the same frequency. Assume that the speed of sound in air is 340 m/s. When the listener is at rest, he/she hears beats with frequency 6 Hz. The listener is moving towards speaker B with a constant speed of 5 m/s, he/she hears no beat (same frequency from both speakers).

a) What is the frequency of speaker A?

Now the listener is at rest, but the speaker B moves at a constant speed in the same direction that connects A and L. Speed is positive to the right (see the figure), otherwise it is negative.

b) What is the speed of the sound source B (m/s) so that the listener does not hear beats?

a) So $f_beat=abs(f_A-f_B)=6$. Since the listener does not here at beat when moving toward B $f_A=f_B$ here. Then I use the formula for doppler effect:

$f_L=\frac{340 m/s -5 m/s}{340 m/s}*f_A$ (1) and $f_L=\frac{340 m/s+5 m/s}{340}*f_B$ (2). I use the fact that $f_B=f_A-6$ and set the equations 1 and 2 equal each other and get that $f_A=207 Hz$.

b) I don't get the right answer for this problem. I do almost the same like I did in a) :

$f_L=\frac{340 m/s+0}{340 m/s+0}*207 Hz$ and $f_L=\frac{340 m/s+0}{340 m/s +v_B}*(207-6)Hz$ and I get that $v_B=9.8 m/s$. But this is not correct according to my teacher. Does anyone have some tips?

 

[Kolika28]

Ohh, I see now? Can it be that I forgot a minus sign in the answer?

 

[haruspex]

Ohh, I see now? Can it be that I forgot a minus sign in the answer?

Certainly the solution to your equation is negative, and the answer should be negative since B has the lower frequency, and will have to move left to sound as high.

 

[Kolika28]

Certainly the solution to your equation is negative, and the answer should be negative since B has the lower frequency, and will have to move left to sound as high.

Thank you for your help!