Question

Two cars are moving towards each other at the speed of $ 50\, \text{m/s} $. If one of the cars blows a horn at a frequency of $ 250\, \text{Hz} $, what is the wavelength of the sound perceived by the driver of the other car?
(Speed of sound in air = $ 350\, \text{m/s} $)

• A. 18.7 cm
• B. 105 cm
• C. 75 cm
• D. 10.5 cm

Hint:

When both source and observer move towards each other, frequency increases and wavelength = \( \frac{v}{f'} \)

Answer 1

The Correct Option is B

Using the Doppler effect: Both source and observer are moving towards each other, so: \[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \Rightarrow f' = 250 \cdot \left( \frac{350 + 50}{350 - 50} \right) = 250 \cdot \left( \frac{400}{300} \right) = 250 \cdot \frac{4}{3} = 333.33\, \text{Hz} \] Wavelength observed: \[ \lambda = \frac{v}{f'} = \frac{350}{333.33} \approx 1.05\, \text{m} = 105\, \text{cm} \]