A source emits f0 = 500 Hz and moves toward a stationary observer at 30 m/s in air (v = 330 m/s). What is the observed frequency?

A source emits f0 = 500 Hz and moves toward a stationary observer at 30 m/s in air (v = 330 m/s). What is the observed frequency?

• A. 525 Hz
• B. 550 Hz
• C. 600 Hz
• D. 545 Hz

Answer: (B)

The main idea is the Doppler effect for a moving sound source. When the source moves toward the observer, the sound waves in front of it get squeezed, so the wavelength in the observer’s frame shortens and the frequency increases. The observed frequency is f' = f0 × v / (v − vs), where v is the wave speed in the medium and vs is the source speed toward the observer. Here, f0 = 500 Hz, v = 330 m/s, and vs = 30 m/s toward the observer. So f' = 500 × 330 / (330 − 30) = 500 × 330 / 300 = 500 × 1.1 = 550 Hz. If the observer moved instead, or if the source moved away, the numbers would change accordingly (for example, moving away would lower the observed frequency). The given scenario yields 550 Hz as the observed frequency.

The main idea is the Doppler effect for a moving sound source. When the source moves toward the observer, the sound waves in front of it get squeezed, so the wavelength in the observer’s frame shortens and the frequency increases. The observed frequency is f' = f0 × v / (v − vs), where v is the wave speed in the medium and vs is the source speed toward the observer.

Here, f0 = 500 Hz, v = 330 m/s, and vs = 30 m/s toward the observer. So f' = 500 × 330 / (330 − 30) = 500 × 330 / 300 = 500 × 1.1 = 550 Hz.

If the observer moved instead, or if the source moved away, the numbers would change accordingly (for example, moving away would lower the observed frequency). The given scenario yields 550 Hz as the observed frequency.