A small source of sound vibrating at a frequency 500   H z is rotated along a circle of radius 100…

In one case the source is moving away and in one case this is moving towards while the observer is in rest so using Doppler shift in sound,

$f=f_0\left(\frac{v}{v\pm v_s}\right)$,

here the angular velocity is given,

$\omega =$$5 \mathrm{rev} {\mathrm{s}}^{-1}$ and the radius of the circle is, $\frac{1}{\pi } \mathrm{m}$

so the velocity of the source is,

$v_s=\omega r=5\times \frac{1}{\pi }=1.59 \mathrm{m} {\mathrm{s}}^{-1}$

so apparent frequency,

$f=f_0\left(\frac{v}{v\pm v_s}\right)=500\left(\frac{332}{332\pm 1.59}\right)=485.4 \mathrm{Hz} \& 515.5 \mathrm{Hz}$