Question

An observer moves towards a stationary source of sound with a velocity \(\left(\frac{1}{5}\right)^{th}\) of the velocity of sound. The percentage increase in the apparent frequency is

• A. \(0.5\%\)
• B. \(0\%\)
• C. \(20\%\)
• D. \(5\%\)

Hint:

For an observer moving towards a stationary source, the apparent frequency is \(f(v+v_{o})/v\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For an observer approaching a stationary source, \(f'=f\left(\dfrac{v+v_{o}}{v}\right)\).

Step 2: Substitute
With \(v_{o}=\dfrac{v}{5}\), \(f'=f\left(1+\dfrac{1}{5}\right)=1.2f\).

Step 3: Percentage Change
\(\dfrac{f'-f}{f}\times 100=\dfrac{0.2f}{f}\times 100=20\%\)

Step 4: Compare the options
The increase is \(20\%\), option (C).

Final Answer:
The apparent frequency increases by 20 percent. \[ \boxed{\text{(C) }20\%} \]