An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the X axis. They are pulled from the equilibrium position in opposite directions along the X axis by a small angular amplitude _0= ^ -1 (0.9) and r

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An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the X axis. They are pulled from the equilibrium position in opposite directions along the X axis by a small angular amplitude _0= ^ -1 (0.9) and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 ~m / s , the maximum variation in the frequency (in Hz ) as measured by the receiver (Take the acceleration due to gravity g=10 ~m / s ^2 ) is

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Correct answer: A. A

aligned & _0=1- _0^2 2 =0.9 \ & _0^2 2 =0.1 _0=10.2= 1 5 aligned aligned & f_ = v+v^ v-v^ f \ & f_ = v-v^ v+v^ f \ & f_ =f_ -f_ = v+v^ v-v^ f- v-v^ v+v^ f \ & = (v+v^ )^2- (v-v^ )^2 v^2-v^ 2 f aligned f_ = 4 v v^ v^2-v^ 2 f ....(i) Here, v ^ = _ = _0 ( = angular frequency ) aligned & = _0 ~g \ & v ^ = _0 ~g \ & v ^ = 1 5 10 8 \ & v ^ =4 aligned Put in equation (i) aligned & f _ = 4 330 4 660 330^2-4^2 \ & 16 330 660 330 32 aligned

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