The shinkansen, the japanese "bullet" train, runs at high speed from tokyo to nagoya. riding on the
shinkansen, you notice that the frequency of a crossing signal changes markedly as you pass the crossing. as you approach the crossing, the frequency you hear is f; as you recede from the crossing the frequency you hear is 2f/3. what is the speed of the train?

68.6 m/s

Explanation:

We have the following data:

is the speed of the train

is the speed of sound in air

is the frequency of the source of sound (the stationary signal)

is the required frequency

Now, this can be expressed mathematically as follows:

When the train approaches the source of sound the frequency is :

(1)

When the train recedes the source of sound the frequency is :

(2)

Let's divide (1) by (2) to simplify and the find :

(3)

Isolating :

(4)

(5)

Finally:

This is the speed of the train

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at position d, potential energy is maximum.

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