91Ó°ÊÓ

The apparent frequency of a moving source increases when the source moves towards the listener. This change in apparent frequency is the Doppler effect.

The frequency is\(f = 3500\;{\rm{Hz}}\).

The speed of the ambulance is\({v_s} = 1200\;{\rm{km/h}} = 333.3\;{\rm{m/s}}\).

The speed of sound is\(v = 342\;{\rm{m/s}}\).

The speed of the listener is zero.

(a)

The Doppler Effect tells the apparent frequency is,

\(f' = f\left( {\frac{{v - {v_o}}}{{v - {v_s}}}} \right)\)

Now, the apparent frequency is,

\(\begin{array}{c}f' = 3500\left( {\frac{{342 - 0}}{{342 - 333.3}}} \right)\\ = 3500 \times \frac{{1140}}{{29}}\\ = 137586.2\;{\rm{Hz}}\end{array}\)

Hence, the apparent frequency is\(137586.2\;{\rm{Hz}}\)

(b)

Now, the apparent frequency of the passing away ambulance is,

\(\begin{array}{c}f'' = 3500\left( {\frac{{342 - 0}}{{342 - \left( { - 333.3} \right)}}} \right)\\ = 3500 \times \frac{{1140}}{{2251}}\\ = 1772.5\;{\rm{Hz}}\end{array}\)

Hence, the apparent frequency is \(1772.5\;{\rm{Hz}}\)