Question

A source of sound is moving towards a stationary observer with $\left(\frac{1}{10}\right)^{\text{th}}$ the speed of sound. The ratio of apparent to real frequency is

• A. 10 : 9
• B. 11 : 10
• C. 9 : 10
• D. 10 : 11

Hint:

When the source moves toward the observer, the frequency increases, so the ratio must be greater than 1.

Answer 1

The Correct Option is A

Step 1: According to the Doppler Effect, when a source of sound moves towards a stationary observer, the apparent frequency ($f'$) is given by: \[ f' = f \left( \frac{v}{v - v_s} \right) \] where $v$ is the speed of sound, $v_s$ is the speed of the source, and $f$ is the real frequency.
Step 2: Given that the source speed is $\frac{1}{10}$ of the speed of sound: \[ v_s = \frac{v}{10} = 0.1v \]
Step 3: Substitute the value of $v_s$ into the formula to find the ratio $\frac{f'}{f}$: \[ \frac{f'}{f} = \frac{v}{v - 0.1v} \]
Step 4: Simplify the fraction: \[ \frac{f'}{f} = \frac{v}{0.9v} = \frac{1}{0.9} = \frac{10}{9} \] Therefore, the ratio is $10 : 9$.