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This phenomenon is crucial for understanding sound and light waves, with applications ranging from radar technology to astronomy.
When a sound source moves, the wavefronts it emits become compressed in the direction of motion and spread out behind it.
The speed of the wave is determined by the medium (e.g., air) and not by the motion of the source or observer.g., air) and not by the motion of the source or observer.
A car with a siren emitting sound at 500 Hz moves towards a stationary observer at $20 \text{ m s}^{-1}$. The speed of sound is $340 \text{ m s}^{-1}$.
What frequency does the observer hear?
Solution
$$f' = f \frac{v}{v - u_s} $$
$$= 500 \frac{340}{340 - 20}$$
$$ = 500 \frac{340}{320} \approx 531.25 \text{ Hz}$$
When the observer moves, the speed of the wave relative to the observer changes.
An observer runs towards a stationary siren emitting sound at 500 Hz with a speed of $10 \text{ m s}^{-1}$. The speed of sound is $340 \text{ m s}^{-1}$.
What frequency does the observer hear?
Solution
$$f' = f \frac{v + u_o}{v}$$
$$= 500 \frac{340 + 10}{340}$$
$$ = 500 \frac{350}{340} \approx 514.7 \text{ Hz}$$
The key to understanding the Doppler effect lies in the relative motion between the source and the observer.
Doppler effect
The Doppler effect is the change in the observed frequency of a wave when there is relative motion between the source and the observer