Question

A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity of 17 m/s. The apparent change in the wavelength of sound heard by the observer is (speed of sound in air = 340 m/s):

• A. 0.1 m
• B. 0.2 m
• C. 0.4 m
• D. 0.5 m

Hint:

The apparent wavelength change for a moving source can be calculated using the Doppler effect equation.

Answer 1

The Correct Option is B

Step 1: Use the Doppler effect formula.
When the source of sound is approaching the observer, the apparent frequency \( f' \) is given by the Doppler effect equation: \[ f' = f \left( \frac{v + v_s}{v} \right) \] where \( f \) is the frequency of the source, \( v \) is the speed of sound, and \( v_s \) is the velocity of the source.

Step 2: Calculate the wavelength change.
The change in wavelength \( \Delta \lambda \) can be found using the relation \( \Delta \lambda = \frac{v}{f} - \lambda_0 \), where \( \lambda_0 \) is the initial wavelength.

Step 3: Apply the values.
Given \( f = 170 \, \text{Hz} \), \( v = 340 \, \text{m/s} \), and \( v_s = 17 \, \text{m/s} \), the apparent wavelength change is: \[ \Delta \lambda = \frac{340}{170} \times \left( \frac{340 + 17}{340} \right) \approx 0.2 \, \text{m} \]