Physics

Problem

Which of the following correctly states the relationship between the observed frequency

f_\text{obs}

and the rest frequency

f_0

of a siren when the source moves directly toward a stationary listener in still air? a)

f_{\text{obs}}=f_0

because the wavelength of the sound does not change in air. b)

f_{\text{obs}}<f_0

because the speed of sound decreases for a moving source. c)

f_{\text{obs}}>f_0

because successive wavefronts reach the listener in less time. d)

f_{\text{obs}}>f_0

because the siren’s motion increases the speed of the sound waves it emits.

Intuitive explanation

The Doppler effect describes how motion compresses or stretches sound waves. When a source moves toward you, the wavefronts bunch up in front of it, so you encounter more waves per second than the source actually emits—meaning the observed frequency increases. The key is recognizing that the wavelength shrinks while the wave speed stays constant in still air, forcing frequency upward: $f_\text{obs} > f_0$ .

Intuitive explanation

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