Question 16

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 $\theta_0 = \cos^{-1}(0.9)$ 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 ___