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An opera singer in a convertible sings a note at 600 Hz while cruising down the highway at 100 km/h . The speed of sound n the air is 343 m/s. What is the frequency heard by a person standing beside the road in front of the car?

User Genea
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1 Answer

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Final answer:

The frequency heard by a person standing beside the road in front of the car can be calculated using the formula for the Doppler effect. In this case, the frequency heard is approximately 592.3 Hz.

Step-by-step explanation:

The frequency heard by a person standing beside the road in front of the car is different from the frequency emitted by the opera singer.

The frequency heard by the person standing beside the road can be calculated using the formula for calculating the apparent frequency observed due to the Doppler effect:

f' = f(v + vr) / (v + vs)

Where:

  • f' is the apparent frequency observed
  • f is the frequency emitted by the opera singer
  • v is the speed of sound in air
  • vr is the velocity of the person standing beside the road
  • vs is the velocity of the opera singer

In this case, the opera singer is in a convertible moving at 100 km/h, so the velocity of the opera singer (vs) is 100 km/h. The speed of sound (v) is 343 m/s. The velocity of the person standing beside the road (vr) is 0 m/s since they are stationary. The frequency emitted by the opera singer (f) is 600 Hz.

Using these values in the formula, we can calculate the apparent frequency observed by the person standing beside the road:

f' = 600 Hz * (343 m/s + 0 m/s) / (343 m/s + 100 km/h)

Simplifying the equation gives:

f' = 600 Hz * 343 m/s / (343 m/s + 27.8 m/s)

The apparent frequency observed by the person standing beside the road is approximately 592.3 Hz.

User Murb
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