Consider two tuning forks with natural frequency 250 ~Hz . One is moving away and another is moving towards a stationary observer at same speed. If the observer hears beats of frequency 5 ~Hz , then the speed of the tuming fork is : (Given, speed of sound wave is 350 ~m / s .)

Step-by-step solution

Given, speed of sound, v=350 ~m / s , actual frequency, n₀=250 ~Hz and number of beats heared, x=5 As source is moving towards the observer therefore, the apparent frequency, n₁=n₀ v v-v_s Similarly, as source is moving away from the observer, therefore the apparent frequency, n₂= n₀ v v+v_s Beats heared by the observer, x=n₁-n₂ Hence, from the Eq. (i) and (ii), we get, aligned x= & n₀ v [ 1 v-v_s - 1 v+v_s ] x= & n₀ v [ v+v_s-v+v_s v^2-v_s^2 ] & x=n₀ v [ 2 v_s v^2-v_s^2 ] & x (v^2-v_s^2 )=n₀ v (2 v_s ) aligned whe