Exploring the Doppler Effect and Beat Frequencies in Sound Waves

[IIK*JII]

Homework Statement

In the figure, a motionless observer stands between sound sources A and B, which oscillate at 338 Hz and 342 Hz, respectively. The observer hears a beat. Next, when the observer begins moving at a constant speed on the straight line connecting A and B, the beat is no longer heard. Here, the speed of sound in air is 340 m/s

Homework Equations

f_b=|f_B-f_A|...(1)

Doppler equation
f'= f($\frac{v\pm v0}{v\mp vs}$)

v0 = observer's speed

The Attempt at a Solution

1st, I assume that observer walking towards A in order not to hear beat frequency.

Thus, f$^{'}_{A}$=f_A($\frac{v+v0}{v}$) (2)
f$^{'}_{B}$=f_B($\frac{v-v0}{v}$) (3)

from (1); f_b = |338-342|=4 Hz
so |(2) - (3)| = 4 Hz and I got only 1 unknown to solve
∴v0 = 4 m/s
but the answer is 2 m/s toward A, Oh! Did I do wrong way or my assumption was wrong??

 

[Yukoel]

Hello IIK*JII
When the observer doesn't hear beats its frequency should be zero or the two frequencies should be equal ,right?I am getting 2m/s as well if my calculations are not wrong. Maybe you have messed up your calculations somewhere by the looks of your method I suspect you have inverted the situation and still getting 4 beats .
Rest is all correct .Even if you had assumed that observer walked towards B you'd getting the same answer in negative.
Correct me if I am wrong.
regards
Yukoel

 

[IIK*JII]

Yukoel !

Okay, I understand it because I inverted the situation..

Thanks a lot :)