Frequency of source, \(v_{0}=100 \mathrm{Hz}\)
Velocity of source, \(v_{s}=19.4 \mathrm{ms}^{-1}\)
Velocity of sound in air, \(v=330 \mathrm{ms}^{-1}\)
As the velocity of source along the source observer line is \(v_{s} \cos 60^{\circ}\) and the observer is at rest, so the apparent frequency observed by the observer is
\({v=v_{0}\left(\frac{v}{v-v_{s} \cos 60^{\circ}}\right)}\)
\({=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{330 \mathrm{ms}^{-1}-\left(19.4 \mathrm{ms}^{-1}\right)\left(\frac{1}{2}\right)}\right)}\)
\({=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{330 \mathrm{ms}^{-1}-9.7 \mathrm{ms}^{-1}}\right)}\)
\({=(100 \mathrm{Hz})\left(\frac{330 \mathrm{ms}^{-1}}{320.3 \mathrm{ms}^{-1}}\right)=103 \mathrm{Hz}}\)
$ {z_1} = A\sin (kx - \omega \,t) $ , $ {z_2} = A\sin (kx + \omega \,t) $ , $ {z_3} = A\sin (ky - \omega \,t) $ .