Question: A person on a railroad car blows a trumpet note at 440Hz. The car is moving toward a wall at$20.0\frac{m}{s}$. Find the sound frequency (a)at the wall and (b) reflected back to the trumpeter.

• i)The frequency of a trumpet is$f=440Hz$
• ii) The speed of the car is$V_S=20.0\frac{m}{s}.$ .

Use the principle of the Doppler Effect and its corresponding equations.

Formula:

The frequency received by the observer or the source according to Doppler’s Effect, (when detector at rest and source is approaching detector)

$f\text{'}=f\times \frac{V}{V-V_S}$ (i)

(Consider source at rest and detector is approaching source)

$f\text{'}=f\times \frac{V+V_D}{V}$ (ii)

Here, the wall is the detector and the car is the source of sound.

Consider the equation of Doppler Effect for stationary detector and moving source using equation (i) as:
$$\begin{gathered} f\text{'}=440\times \frac{343}{343-20.0} \\ =467Hz \end{gathered}$$

Hence, the value of the sound frequency is 467 Hz.

Here, the reflected wave fromthewall is a source and the trumpeter in the car isthedetector.

Consider equation (ii) of Doppler Effect for stationary source and moving detector as:

$$\begin{gathered} f\text{'}=467\times \frac{343-(-20)}{343} \\ =494Hz \end{gathered}$$

Hence, the value of the reflected frequency is 494Hz.