Question

A sound source is moving towards a stationary listener with \( \frac{1}{10} \)th of the speed of sound. The ratio of apparent to read frequency is:

• A. \( \left( \frac{9}{10} \right)^2 \)
• B. \( \left( \frac{10}{9} \right) \)
• C. \( \left( \frac{11}{10} \right)^2 \)
• D. \( \left( \frac{10}{9} \right)^2 \)

Hint:

For a sound source moving towards the observer, the frequency observed increases, and the ratio is given by the Doppler effect formula.

Answer 1

The Correct Option is B

Step 1: Doppler effect formula.
The Doppler effect equation for frequency when the source is moving towards the observer is given by: \[ f' = \frac{f}{1 - \frac{v_s}{v}} \] where \( f' \) is the observed frequency, \( f \) is the original frequency, \( v_s \) is the speed of the source, and \( v \) is the speed of sound.

Step 2: Apply the given values.
Since the source is moving towards the observer at \( \frac{1}{10} \)th of the speed of sound, the ratio of the apparent to read frequency is \( \frac{10}{9} \). Thus, the correct answer is (2).