A girl is sitting near the open window of a train that is...

A girl is sitting near the open window of a train that is moving at a velocity of 10.00 $\mathrm{m} / \mathrm{s}$ to the east. The girl's uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 500.0 $\mathrm{Hz}$ . The air is still. (a) What frequency does the uncle hear? (b) What frequency does the girl hear? A wind begins to blow from the east at 10.00 $\mathrm{m} / \mathrm{s} .$ (c) What frequency does the uncle now hear? (d) What frequency does the girl now hear?

A girl is sitting near the open window of a train that is moving at a velocity of 10.00 $\mathrm{m} / \mathrm{s}$ to the east. The girl's
uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 500.0 $\mathrm{Hz}$ . The air is
still. (a) What frequency does the uncle hear? (b) What frequency
does the girl hear? A wind begins to blow from the east at 10.00
$\mathrm{m} / \mathrm{s} .$ (c) What frequency does the uncle now hear? (d) What frequency does the girl now hear?

Key Concepts

Wind Influence on Sound Waves

Wind can alter the effective velocity of sound waves by either aiding or opposing the motion of the wave relative to an observer or source. When wind is present, it adds or subtracts from the speeds of the source and observer relative to the medium, thus modifying the frequencies observed as a result of the Doppler Effect.

Sound Propagation in a Medium

Sound waves require a medium (such as air) to travel, and their speed is determined by the properties of that medium. Because the speed of sound is defined relative to the medium, any movement of the medium (for example, wind) alters the effective speed of sound relative to the observer and the source.

Reference Frames and Relative Motion

In problems involving the Doppler effect, it is crucial to analyze the motion of both the source and the observer relative to the medium through which the sound propagates. The speeds of both the observer and the source must be considered with respect to the air (or medium), rather than just their speeds relative to each other.

Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. This principle explains why the observed frequency of a sound (or light) is higher when the source and observer are moving toward each other and lower when they are moving apart.

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