Doppler Effect: Sound Source Moving Towards Observer

This question relates to the Doppler Effect, which describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.

Understanding the Scenario

We have a stationary man (observer) and a sound source that is moving towards him. We need to determine how the frequency of the sound perceived by the man changes compared to the original frequency emitted by the source.

Explanation of the Doppler Effect in this Case

• When the sound source moves towards a stationary observer, the sound waves it emits get compressed in the direction of motion.
• Imagine the source emitting wave crests at regular intervals. As the source moves towards the observer, each subsequent crest is emitted from a position closer to the observer than the previous one.
• This compression of waves means that the distance between successive wave crests (the wavelength) reaching the observer decreases.
• Since the speed of sound in the medium remains constant, a shorter wavelength corresponds to a higher frequency (frequency is inversely proportional to wavelength: \( f = \frac{v}{\lambda} \), where \( f \) is frequency, \( v \) is the speed of sound, and \( \lambda \) is wavelength).
• Therefore, the stationary observer perceives the sound waves arriving more frequently than if the source were stationary.

Conclusion

As a result of the sound source moving towards the stationary man, the frequency of the sound appears higher than the original frequency.