I need help with this question.

A commuter train blows its horn as it passes a passenger platform at a constant speed of 55.0 m/s. The train horn sounds at a frequency of 350 Hz when the train is at rest.
(a) What is the frequency observed by a person on the platform as the train approaches?

(b) What is the frequency observed by a person on the platform as the train recedes from him?

(c) What wavelength does the observer find in each case?

To answer these questions, we need to use the formula for the Doppler effect. The Doppler effect describes the change in frequency and wavelength of waves due to the relative motion between the source of the waves and the observer.

The formula for the frequency observed by an observer when the source is in motion is given by:

f' = (v + vo) / (v - vs) * f

where:
f' is the observed frequency,
f is the frequency emitted by the source,
v is the speed of sound in air (approximately 343 m/s),
vo is the velocity of the observer relative to the medium (positive when towards the source),
and vs is the velocity of the source relative to the medium (positive when towards the observer).

Let's use this formula to answer each part of the question.

(a) When the train is approaching the platform:
- The source is the train horn.
- The observer is the person on the platform.
- The velocity of the observer relative to the medium (vo) is 0 since the person is stationary.
- The velocity of the source relative to the medium (vs) is positive 55.0 m/s since the train is approaching.
- The frequency emitted by the train horn (f) is 350 Hz.

Using the formula, we can calculate the observed frequency (f'):

f' = (343 + 0) / (343 - 55) * 350

(b) When the train is receding from the platform:
- The source is still the train horn.
- The observer is still the person on the platform.
- The velocity of the observer relative to the medium (vo) is still 0 since the person is stationary.
- The velocity of the source relative to the medium (vs) is now negative 55.0 m/s since the train is receding.
- The frequency emitted by the train horn (f) is still 350 Hz.

Using the formula again, we can calculate the observed frequency (f').

f' = (343 + 0) / (343 + 55) * 350

(c) The wavelength can be found using the formula:

λ' = v / f'

where:
λ' is the observed wavelength,
v is the speed of sound in air, and
f' is the observed frequency calculated in parts (a) and (b).

Using this formula, we can find the wavelength observed in each case.