BITSAT 2015 Paper

Let v = speed of sound and $v_S$ = speed of tuning forks. Apparent frequency of fork moving towards the observer is $n_1$ = $\left(\frac{v}{v-v_s}\right)$ n Apparent frequency of the fork movingaway from the observer is $n_2$ = $\left(\frac{v}{v+v_s}\right)$ n If f is the number of beats heard per second. then f = $n_1 - n_2$ ⇒ f = $\left(\frac{v}{v-v_s}\right)$ n - $\left(\frac{v}{v+v_s}\right)$ n ⇒ f = $\frac{v(v+v_s)-v(v-v_s)}{v^2-v_s^2}$ (n) ⇒ $\frac{2vv_s n}{v^2-v_s^2}$ = f ⇒ 2 $\left(\frac{v_s}{v}\right)$ = n = f {if $v_s$ ≪ v} ⇒ $v_5$ = $\frac{fv}{2n}$ putting v = 340 m/s, f = 3, n = 340 Hz we get, $v_s$ = $\frac{340\times3}{3\times340}$ = 1.5 m/s