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In which of the following situations would an observer perceive no change in frequency of a sound wave?

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Final answer:

An observer perceives no change in frequency when there is no relative motion between the source and observer, as in the case of people on the same vehicle moving at the same speed or when both are stationary relative to the moving air between them.

Step-by-step explanation:

Doppler Effect and Frequency Perception

An observer perceives no change in frequency of a sound wave in a situation where the source and observer are moving together or have no relative motion between them. The classic example is a conversation between a driver and passenger on a motorcycle. They experience no Doppler shift because they are moving at the same speed and in the same direction. This phenomenon is consistent with the observer moving together with the sound source, such as an engineer on a train hearing the train's whistle.

When an observer moves toward or away from a stationary source of sound, the perceived frequency changes. If moving towards the source, the frequency appears higher, and if moving away, it appears lower. This is a primary manifestation of the Doppler effect. However, when there is no relative movement, as explained earlier, no change in frequency is observed.

The Doppler effect also does not occur when sound moves through moving air between two people if both are stationary relative to the air itself. The key factor is the absence of relative motion between the observer and the source of sound.

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