gen-define-the-doppler-effect-and-give-one-short-worked-example-9eed

Define the Doppler effect and give one short worked example.

# Doppler Effect **Definition:** The Doppler effect is the change in observed frequency (or wavelength) of a wave when there is relative motion between the source of the wave and the observer. When the source and observer move closer together, the observed frequency increases; when they move apart, the observed frequency decreases. ## Formula For sound waves with source moving: $$f' = f \left(\frac{v}{v \mp v_s}\right)$$ where: - f' = observed frequency - f = source frequency - v = speed of sound - v_s = speed of source (− if approaching, + if receding) ## Worked Example **Problem:** An ambulance siren emits sound at 800 Hz. The ambulance drives toward a stationary observer at 30 m/s. What frequency does the observer hear? (Speed of sound = 340 m/s) **Solution:** - f = 800 Hz - v = 340 m/s - v_s = 30 m/s (approaching, so use minus sign) $$f' = 800 \left(\frac{340}{340 - 30}\right)$$ $$f' = 800 \left(\frac{340}{310}\right)$$ $$f' = 800 \times 1.097 = 878 \text{ Hz}$$ The observer hears a frequency of **878 Hz**, higher than the emitted 800 Hz because the ambulance is approaching.