Driving down a quiet street on a summer day with the car windows down, you see a convertible approaching from the opposite direc

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Driving down a quiet street on a summer day with the car windows down, you see a convertible approaching from the opposite direc

tion, with the driver playing her car stereo loudly. Having a well-trained musician’s ear, you notice that the song you hear is in a key one semitone (the interval between two adjacent keys on a piano) above the key in which the song is typically heard. You also know that to shift any note by one semitone, the frequencies must be related by a factor of 1.06. Assume both drivers are traveling at the same speed, what is their speed?

Physics

1 answer:

ValentinkaMS [2.4K] · Answer 1 · 2026-03-15T22:06:06+03:00

The ratio of the perceived frequency to the actual frequency is 1.06. Denote their speeds as v. Based on the Doppler effect formula applicable to a sound source and listener moving toward each other: n = n₀ (V + v) / (V - v) where V represents the speed of sound at 340 m/s. Thus, n / n₀ = (V + v) / (V - v), which leads to 1.08 = (360.4 - 1.06 v)/(340 + v); solving yields v = 9.9 m/s.