Question

Two identical cars are driving toward one another and sounding their horns. You’re the driver of one of the cars. You measure your car’s horn to be sounding at 512 Hz, but you measure the horn of the other car to be sounding at 600. Hz. The speed of sound is 345 m/s. If you are traveling at 26.8 m/s (60 mph), how fast is the other car traveling?

Answer 1

The speed at which the other car is travelling is 27.71 m/s.

Speed of the second car

The speed of the second car is calculated as follows;

f₂ = f₁(v + v₁)/(v - v₂)

where;

• f₂ is the frequency of second car
• f₁ is frequency of first car
• v is speed of sound
• v₁ is speed of first car
• v₂ is speed of second car

600 = 512(345 + 26.8) / (345 - v₂)

600/512 = (345 + 26.8) / (345 - v₂)

1.1718 = 371.8/(345 - v₂)

345 - v₂ = 371.8/1.1718

345 - v₂ = 317.289

v₂ = 345 - 317.289

v₂ = 27.71 m/s

Thus, the speed at which the other car is travelling is 27.71 m/s.

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