Question

When the observer moves towards a stationary source with velocity \( V_o \), the apparent frequency of emitted note is \( F_1 \). When the observer moves away from the source with velocity \( V_o \), the apparent frequency is \( F_2 \). If \( V \) is the velocity of sound in air and \( \frac{F_1}{F_2} = 2 \), then \( \frac{V}{V_o} \) is equal to

• A. 5
• B. 6
• C. 4
• D. 3

Hint:

When solving Doppler effect problems, carefully apply the correct formula for moving observers and sources, and use the given ratios to find unknown velocities or frequencies.

Answer 1

The Correct Option is D

Step 1: Understanding the Doppler effect.
The Doppler effect explains the change in the frequency of sound when the source or the observer is moving. The formula for the apparent frequency when the observer moves towards or away from the source is: \[ F = F_0 \left( \frac{V + V_o}{V} \right) \] where \( F_0 \) is the emitted frequency, \( V_o \) is the velocity of the observer, and \( V \) is the speed of sound in air.
Step 2: Using the given ratio.
The given ratio is \( \frac{F_1}{F_2} = 2 \). This indicates that the change in frequency depends on the relative velocities of the observer and the source. By solving the equation for \( \frac{V}{V_o} \), we find that the value of \( \frac{V}{V_o} = 3 \).
Step 3: Conclusion.
Thus, the correct answer is (D) 3.