Using your knowledge of the Doppler effect, is the sound of a firetruck's siren higher pitch when it is moving toward you or away from you?

Question

BlackTom AI · Accepted Answer

The Doppler effect causes the apparent frequency to increase when a sound source moves toward an observer and decrease when it moves away, so the siren sounds higher in pitch as the firetruck approaches. 1) Relevant concepts - Doppler effect: change in observed frequency due to relative motion between source and observer. - For a moving source and stationary observer, observed frequency f' = f · v/(v − vs) when the source moves toward the observer, and f' = f · v/(v + vs) when it moves away. Here v is the speed of sound in air and vs is the source speed. - Physically: wavefronts get compressed in front of the moving source (shorter wavelength → higher frequency) and stretched behind it (longer wavelength → lower frequency). 2) Step-by-step reasoning - Start with the formula for a moving source and stationary listener: f' = f · v/(v ∓ vs), choose the minus sign when the source approaches (because distance between successive crests hitting the observer is reduced). - When the truck moves toward you, denominator is (v − vs) < v, so v/(v − vs) > 1, hence f' > f (higher pitch). - When it moves away, denominator is (v + vs) > v, so v/(v + vs) < 1, hence f' < f (lower pitch). 3) Numerical example (intermediate steps) - Let f = 1000 Hz (siren frequency), v = 343 m/s, vs = 30 m/s. - Approaching: f' = 1000 · 343/(343 − 30) = 1000 · 343/313 = 1000 · 1.0958 ≈ 1096 Hz. - Receding: f' = 1000 · 343/(343 + 30) = 1000 · 343/373 = 1000 · 0.9193 ≈ 919 Hz. - These calculations show a clear increase when approaching and decrease when receding. 4) Why the correct answer is correct - Mathematical formula and physical wavefront reasoning both show approaching motion produces compressed wavelengths and a higher observed frequency (higher pitch). 5) Why other options are incorrect - "Away": incorrect because moving away produces stretched wavefronts and a lower observed frequency (as shown numerically). - "Stays the same": incorrect because relative motion changes the spacing of wavefronts; only if there is no relative motion would pitch remain unchanged. 6) Conclusion Observed pitch is higher when the firetruck is moving toward you; this matches the provided answer: toward.

Using your knowledge of the Doppler effect, is the sound of a firetruck's siren higher pitch when it is moving toward you or away from you?单项选择题

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