A source S emitting sound of 300 Hz is fixed of block A which is attached to free end of a spring `S_A` as shown in the figure. The detector D fixed on block B attached to the free end of spring `S_B` detects this sound.
The blocks A and B are simultaneously displaced towards each other through of 1.0 m and then left to vibrate. Find the maximum and minimum frequencies of sound detected by D if the vibrational frequency of each block is 2 Hz (velocity of sound is 340 m/s).

Explanation

The motion of A and B is sychronized. Hence the maximum frequencies detected by D will be
`f_(max)=((v+v_D)/(v-v_S))f`
(when S and D are approaching each other while at their equilibrium position.)
`=((340+Aomega)/(340-Aomega))f=((340+12.56)/(340-12.56))xx300=323Hz`
Similarly, the apparent frequency will be minimum when the source and the detector recede from each other with maximum speed `(=Aomega)`
`f_(min)=((v-Aomega)/(v+Aomega))f=((340-12.56)/(340+12.56))xx300=278.6Hz`