A stationary siren, located on a railway station platform, emits sound at a fixed frequency. A physicist monitors the sound from the siren as she passes through the station at constant speed on a train that does not stop at the station. While she is approaching the siren, she measures the frequency of the sound as 572 Hz. After she passes by the siren and is moving away from it, she notes that the frequency she measures has changed to 468 Hz. You may assume an air temperature of 150C (i) What is the frequency of sound that the siren is emitting? (ii) What speed is the train travelling at?

This physics problem involves the understanding and application of the Doppler effect concepts and physics equations to calculate the frequency of a stationary siren and the speed of a passing train. By substituting the measured frequencies into the Doppler effect equation, a system of equations is solved to find the original frequency of the siren and the speed of the train.

Explanation:

This question involves the Doppler effect, which is a shift in frequency and wave length due to the relative speed between a source and an observer. In this case, the source is the stationary siren and the observer is the physicist on the train. Given the frequencies before the physicist passes the siren (f1 = 572 Hz) and after she passes the siren (f2 = 468 Hz), we can find out the frequency of sound that the siren is emitting (f0) and the speed (v) of the train.

For the emitted frequency of the siren, we can use the formula of the Doppler effect:

f = f0 * ((v + vr) / (v + vs))

Where vr is the observer's speed (the speed of the train), vs is the source speed (here it is 0 because the siren is stationary), and v is the speed of sound.

Substituting frequencies f1 and f2 into the above equation when the observer is approaching and receding from the source, we can solve a system of equations to find f0 and vr (the speed of the train).

The concept of the Doppler effect as well as the understanding of the relevant physics formulas and the capacity to solve related math problems are crucial for this high school physics task.

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