A car P travelling at $20 \mathrm{~ms}^{-1}$ sounds its horn at a frequency of $400 \mathrm{~Hz}$. Another car $\mathrm{Q}$ is travelling behind the first car in the same direction with a velocity $40 \mathrm{~ms}^{-1}$. The frequency heard by the passenger of the car $\mathrm{Q}$ is approximately [Take, velocity of sound $=360 \mathrm{~ms}^{-1}$ ]

<p>Using the Doppler effect formula:</p> <p>$f = f_0\left(\frac{c + v_0}{c + v_s}\right)$</p> <p>where</p> <ul> <li>$f$ is the observed frequency (frequency heard by the passenger in car Q)</li> <li>$f_0$ is the source frequency (400 Hz)</li> <li>$c$ is the speed of sound (360 m/s)</li> <li>$v_0$ is the velocity of the observer (passenger in car Q) relative to the medium (air) in the direction of the source (40 m/s)</li> <li>$v_s$ is the velocity of the source (car P) relative to the medium (air) in the direction of the observer (20 m/s, since it&#39;s moving in the same direction as car Q)</li> </ul> <p>Plugging in the values:</p> <p>$f = 400\left(\frac{360 + 40}{360 + 20}\right)$<br/><br/> $f = 400\left(\frac{400}{380}\right)$<br/><br/> $f = 421$</p> <p>So, the observed frequency is 421 Hz.