Question

A source of sound is moving away from a stationary observer with constant velocity 40 m/s. Find frequency heard by observer, if original frequency of source is 400 Hz and speed of sound in air is 360 m/s

• A. 330 Hz
• B. 320 Hz
• C. 360 Hz
• D. 280 Hz

Answer 1

The Correct Option is C

To solve this problem, we need to use the Doppler effect formula for sound. The Doppler effect describes the change in frequency or wavelength of a wave concerning an observer moving relative to the source of the waves. When the source is moving away from the observer, the observed frequency is lower than the actual frequency of the source.

The formula for the frequency heard by the observer when the source is moving away is given by:

\(f' = \frac{f \cdot v}{v + v_s}\)

where:

• \(f'\,\!\) is the observed frequency.
• \(f\,\!\) is the original frequency of the source (400 Hz).
• \(v\,\!\) is the speed of sound in the medium (360 m/s).
• \(v_s\,\!\) is the velocity of the source relative to the medium (40 m/s, moving away).

Plugging in the values, we have:

\(f' = \frac{400 \cdot 360}{360 + 40} = \frac{144000}{400} = 360 \, \text{Hz}\)

Thus, the frequency heard by the observer is 360 Hz.

Hence, the correct answer is 360 Hz.

Let's review why this option is correct:

• The formula used appropriately accounts for the velocity of the moving source and the speed of sound.
• Substituting the given values into the formula provides the required answer.

Incorrect Options:

• 330 Hz, 320 Hz, and 280 Hz are incorrect as they do not result from the described conditions using the Doppler effect formula.