Question

A train whistle is heard at 330Hz as the train approaches town. The train cuts its speed in half as it nears the station, and the sound of the whistle is then 320 Hz.

What is the speed of the train before slowing down?
Express your answer to two significant figures and include the appropriate units.

Answer 1

To determine the speed of the train before slowing down, we can use the Doppler effect formula. Plugging in the given values and solving the equation, we find that the speed of the train is approximately 94.6 m/s.

Step-by-step explanation:

The question is asking for the speed of the train before it slows down. This can be determined using the Doppler effect formula. The formula is given as

f₁ = f₀ (v + v₉) / (v - v₉)

Where f₁ is the observed frequency, f₀ is the actual frequency, v is the speed of sound, and v₉ is the speed of the train. Using the given information, we can plug in the values:

320 = 330 (331 + v₉) / (331 - v₉)

Now we can solve for v₉:

-v₉^2 + 9v₉ + 4,887 = 0

This is a quadratic equation. Solving for v₉ gives us two possible values: v₉ = -51.7 m/s or v₉ = 94.6 m/s. Since the train cannot be moving in the negative direction, we can discard -51.7 m/s as the speed of the train. Therefore, the speed of the train before slowing down is approximately 94.6 m/s.