Question

A stationary observer receives sonic oscillations from two tuning forks one of which approaches and the other recedes with the same velocity. As this place, the observer hears the beats of frequency f = 2.0 Hz. The velocity ( in m/s) of each tuning fork is $\frac{x}{2}$, if their oscillation frequency is $f_0=680Hz$ and the velocity of sound in air is v = 340 m/s. Find x.

Answer 1

Frequency due to $S_1$ is $f\left(\frac{v-o}{v-s}\right)$

where s is the speed of the source $S_1$

Frequency due to $S_2$ is $f\left(\frac{v-o}{v+s}\right)$

where s is the speed of the source $S_2$

given that beats frequency hears by the observer=2

$f(\frac{v}{v-s}-\frac{v}{v+s})=2$

$s=0.5m/s$

$s=\frac{x}{2}=0.5⟹x=1$