Two tuning forks with natural frequencies of `340 Hz` each move relative to a stationary observer. One fork moves away form the observer, while the other moves towards him at the same speed. The observer hears beats of frequency `3 Hz`. Find the speed of the tuning fork.

Two tuning forks with natural frequencies of `340 Hz` each move relati

1.	Two tuning forks with natural frequencies of `340 Hz` each move relative to a stationary observer. One fork moves away form the observer, while the other moves towards him at the same speed. The observer hears beats of frequency `3 Hz`. Find the speed of the tuning fork.
Answer» Let v be the speed of sound and `v_S` the speed of forks. The apparent frequency of fork which moves towards the observer is `n_1=(v)/(v-v_S)n` The apparent frequency of fork which moves away from observer is `n_2=(v)/(v+v_S)n` If x is the number of beats heard per second the `x=n_1-n_2impliesx(v)/(v-v_S)n-(v)/(v+v_S)n` or `x=(v+v_S-(v-v_S))/(v^2-v_S^2)(vn)` or `(2vv_Sn)/(v^2-v_S^2)=x` `2((v_S)/(v))n=x` or `v_S=(vx)/(2n)` Given `v=340(m)/(s)`,`x=3`,`n=340Hz` `v_S=(340xx3)/(2xx340)=1.5(m)/(s)`

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Two tuning forks with natural frequencies of `340 Hz` each move relative to a stationary observer. One fork moves away form the observer, while the other moves towards him at the same speed. The observer hears beats of frequency `3 Hz`. Find the speed of the tuning fork.

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