2023-04-05 Doppler effect

Problem: The alarm bell is ringing every 0.5s, and a person is in a car traveling 72km/h towards the alarm. Given that the speed of sound through the air is 340m/s, how many alarm bells does the person hear per minute?

Analysis: This question is about the influence of the Doppler effect. They already tell us that the alarm cycle is 0.5s, which is equivalent to telling us the frequency of the wave source. At this time, the observer is moving towards the alarm and close to the wave source, so the frequency of the wave received by the observer will be greater than that of the wave source.

Solution: The? period of the wave source is T=0.5s, and the frequency f=1/T = 1/0.5 Hz = 2Hz can be obtained.

According to the doppler effect? formula as f'=(v+v_o)/(v+v_s)*f, v_o=72km/h=20m/s,v_s = 0, v=340 m/s, substitute the data to get f' = 2.12 Hz.

Number of alarm bells heard per minute n=2.12*60\simeq 127.

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