Two automobiles are equipped with the same singlefrequency...

Two automobiles are equipped with the same singlefrequency horn. When one is at rest and the other is moving toward the first at 18 m$/$s, the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency the horns emit? Assume $T =$ 20$^\circ$C.

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Key Concepts

Doppler Effect

The Doppler Effect describes the phenomenon where the observed frequency of a sound wave changes due to the relative motion between the source and the observer. When the source is moving towards the observer, the sound waves are compressed, resulting in a higher observed frequency compared to the emitted frequency.

Beat Frequency

Beat frequency is the result of two sound waves with similar but not identical frequencies interfering with each other. The interference produces a fluctuating sound intensity at a rate equal to the absolute difference between the two frequencies, which can be perceived as periodic variations in volume.

Speed of Sound

The speed of sound in air is a critical parameter that depends on the temperature of the environment. At 20°C, the speed of sound is typically about 343 m/s. This value is essential when applying the Doppler Effect, as it affects the magnitude of the frequency shift observed.

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