a
(a) The linear velocity of Whistle

\({v_S} = r\omega = 1.2 \times 2\pi \frac{{400}}{{60}} = 50\,m/s\)

When Whistle approaches the listener, heard frequency will be maximum and when listener recedes away, heard frequency will be minimum

So, \({n_{\max }} = n\,\left( {\frac{v}{{v - {v_s}}}} \right) = 500\,\left( {\frac{{340}}{{290}}} \right) = 586Hz\)

\({n_{\min }} = \,n\,\left( {\frac{v}{{v + {v_s}}}} \right) = 500\,\left( {\frac{{340}}{{390}}} \right) = 436Hz\)