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 ,

Step-by-step solution

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