The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you to sound lower pitched, like observed in listening to the car horn in the video. The equation for this is f = (c c + v) f 0, where f is the observed frequency (pitch) of the sound, in Hertz c is the speed of sound, about 761 miles per hour, v is the speed of the sound source, in this case the car, in miles per hour f0 is the frequency of the sound when stationary Using a spectrum analyzer, we could determine the observed frequency when the car was driving away was 236 Hz and the stationary frequency was 253 Hz. Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.

Question

Mathematics

Nick Figueroa

25 December, 06:29

The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you to sound lower pitched, like observed in listening to the car horn in the video. The equation for this is f = (c c + v) f 0, where f is the observed frequency (pitch) of the sound, in Hertz c is the speed of sound, about 761 miles per hour, v is the speed of the sound source, in this case the car, in miles per hour f0 is the frequency of the sound when stationary Using a spectrum analyzer, we could determine the observed frequency when the car was driving away was 236 Hz and the stationary frequency was 253 Hz. Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.

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Omari Lawson · Answer 1

Answer: 54.88 mph

Step-by-step explanation: the Doppler effect formulae is given below as

f' = (v + vo) / (v - vs) * f

Where f' = observed frequency = 236 Hz,

f = frequency of sound source (stationary frequency) = 253 Hz.

v = speed of sound in air = 761 mph

Since the car (source) is moving away relative to the observer, vs will have a negative value (-vs)

vo = 0 mph (since the observer is not moving)

By substituting the parameters, we have that

236 = (761+0) / (761 - (-vs)) * 253

236 = (761 / 761 + vs) * 253

By cross multiplication, we have that

236 * (761 + vs) = 761 * 253

761 + vs = 761 * 253 / 236

761 + vs = 192533 / 236

761 + vs = 815.88

vs = 815.88 - 761

vs = 54.88 mph