Explain the Doppler effect for sound when the source moves toward the observer.

• A. The observed frequency increases; f' = f v /(v − v_s) for a moving source toward the observer
• B. The observed frequency decreases.
• C. The observed wavelength increases.
• D. The speed of sound changes.

Answer: (A)

When a sound source moves toward you, the waves in front of it are packed more tightly, so you hear a higher pitch. The source emits crests at a steady interval T = 1/f, but while this interval passes, the source moves toward the observer by a distance v_s T. That means the separation between successive wavefronts that travel toward you is shorter than the usual wavelength in the medium. The new wavelength is λ' = (v − v_s)T, since the waves still move at speed v but the emission points get closer by v_s T each cycle.

The observed frequency is the wave speed divided by the observed wavelength: f' = v / λ' = v / [(v − v_s)T] = f v /(v − v_s). Because v_s is toward you, the denominator is smaller than v, so f' is greater than f. So the pitch goes up as the source approaches.

The speed of sound in the medium stays the same; it’s a property of the medium, not of the motion of the source. The wavelength does not increase; it decreases, and the frequency increases.