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you and your dog are standing on the side of the road. someone approaches in a very fast car playing an eigth octave c on a piccolo (4186 hz). how fast would they have to approach in m/s so that only your dog would hear the piccolo? (hint: it is unrealistically fast.)

User Andrew Cui
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1 Answer

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The car would need to approach at a minimum speed of 730.8 m/s (rounded to the nearest tenth) for the piccolo's sound to shift above your dog's hearing range while remaining audible to the driver

How to solve

Doppler shift formula: f' = f * (c + v) / (c - v), where:

f' is the perceived frequency

f is the original frequency (4186 Hz)

c is the speed of sound in air (343 m/s)

v is the relative velocity of the source (car)

Set f' at your dog's upper hearing limit (45,000 Hz):

45,000 Hz = 4186 Hz * (343 m/s + v) / (343 m/s - v)

Solve for v:

v = (45,000 Hz - 4186 Hz) * 343 m/s / (45,000 Hz + 4186 Hz) ≈ 730.8 m/s

Therefore, the car would need to approach at a minimum speed of 730.8 m/s (rounded to the nearest tenth) for the piccolo's sound to shift above your dog's hearing range while remaining audible to the driver


The Complete Question

You and your dog, with a maximum hearing range of 45,000 Hz, are standing on the side of the road. Someone approaches in a car playing an eighth-octave C on a piccolo (4186 Hz).

At what minimum speed (m/s) would the car have to approach for the piccolo's sound to shift above your dog's hearing range but remain audible to the car's driver (assume a normal human hearing range of 20-20,000 Hz)?

Calculate the speed rounded to the nearest tenth of a meter per second.

Parameters:

Speed of sound in air: 343 m/s

Piccolo frequency: 4186 Hz

Your hearing range: 20-20,000 Hz

Dog's hearing range: 20-45,000 Hz

Minimum frequency audible to driver: 20 Hz

User Lodo
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