Question

A bus is moving with a velocity of 5 m/s towards a wall. The driver blows the horn of frequency 165 Hz. If the speed of sound in air is 335 m/s, then after reflection of the sound wave, the number of beats per second heard by the passengers in the bus will be

• A. 4
• B. 5
• C. 6
• D. 2

Hint:

When sound reflects from a stationary object and both source and observer are moving, Doppler effect is applied twice — once during approach and once during reflection.

Answer 1

The Correct Option is B

Step 1: Identify the given data.
Velocity of bus (source and observer), \( v_s = v_o = 5 \, \text{m/s} \)
Original frequency of horn, \( f = 165 \, \text{Hz} \)
Speed of sound, \( v = 335 \, \text{m/s} \)
The bus is moving towards a stationary wall, so Doppler effect occurs twice (during incidence and reflection).

Step 2: Frequency of sound reaching the wall.
Since the source (bus) is moving towards the wall, the frequency heard by the wall is:
\[ f_1 = f \left( \frac{v}{v - v_s} \right) \] \[ f_1 = 165 \left( \frac{335}{335 - 5} \right) = 165 \left( \frac{335}{330} \right) = 167.5 \, \text{Hz} \]

Step 3: Frequency of reflected sound heard by passengers.
Now the reflected sound acts as a source from the wall, and the passengers (observer) are moving towards it:
\[ f_2 = f_1 \left( \frac{v + v_o}{v} \right) \] \[ f_2 = 167.5 \left( \frac{335 + 5}{335} \right) = 167.5 \left( \frac{340}{335} \right) = 170 \, \text{Hz} \]

Step 4: Calculate number of beats per second.
Beats per second \( = | f_2 - f | \)
\[ \text{Beats} = |170 - 165| = 5 \]

Step 5: Conclusion.
The number of beats heard per second by the passengers is 5.