Question

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.

Short answer

• a) The sound frequency at the wall is 467Hz
• b) The sound frequency reflected back to the trumpeter is 494Hz

Step-by-step solution

Write the given data

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

Determine the concept of the Doppler Effect

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)

Calculate the sound frequency at the wall

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.

b) Determine reflected frequency back to the trumpeter

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.