Two loudspeakers emit 400 Hz notes. One speaker sits on the...

Two loudspeakers emit $400 \mathrm{Hz}$ notes. One speaker sits on the ground. The other speaker is in the back of a pickup truck. You hear eight beats per second as the truck drives away from you. What is the truck's speed?

Key Concepts

Speed of Sound

The Speed of Sound is the rate at which sound waves travel through a medium such as air. This parameter is fundamental in acoustic calculations, including those involving the Doppler Effect, because it provides the basis for determining how a moving source alters the observed frequency relative to the speed of the sound in the given medium.

Relative Motion

Relative Motion refers to the movement of objects and the associated effects from an observer's perspective. In acoustics, it is important for understanding how the speed and direction of a moving sound source can alter the observed frequency, and thereby contribute to phenomena such as the Doppler shift and resulting beat frequencies.

Doppler Effect

The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. This concept explains why a sound from a moving source appears lower in frequency when it is moving away and higher when it is approaching, which is crucial in calculating frequency shifts caused by motion.

Beat Frequency

Beat Frequency is the phenomenon that occurs when two sound waves of slightly different frequencies interfere with each other, resulting in a periodic fluctuation in amplitude. The rate of these fluctuations is equal to the difference in frequencies, making it a useful concept for determining the relative change in frequency due to factors like the Doppler Effect.

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