train is approaching the station at a speed of 20m.s sounds a 220 hz horn. What frequency does an observer on the station platform hear

Frequency is shifted upward by

fo * (V/a)

fo = 220 Hz
a = speed of sound = 340 m/s
V = 20 m/s

f = fo*[1 + (V/a)]

There is a more accurate Doppler shift formula, but this is accurate enough when a<<c, as is the case here.

For the exact formula, see
http://en.wikipedia.org/wiki/Doppler_effect

To calculate the frequency heard by an observer on the station platform, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by someone moving relative to the source of the wave.

In this case, we have a moving train (source of the sound) and an observer on the station platform. The observer is at rest relative to the train and receives the sound waves from the approaching train.

The formula for the Doppler effect in this scenario is as follows:

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

Where:
- f' is the observed frequency
- f is the actual frequency emitted by the moving source (in this case, the horn)
- v is the speed of sound in air (approximately 343 m/s at room temperature)
- vo is the velocity of the observer
- vs is the velocity of the source

From the question, we know that the train is approaching the station. Since the train is approaching, its velocity will be negative (-20m/s).

Substituting the given values into the formula:

f' = 220 Hz * (343 m/s + 0 m/s) / (343 m/s - 20 m/s)

Simplifying the equation:

f' = 220 Hz * 343 m/s / 323 m/s

f' ≈ 233.56 Hz

Therefore, an observer on the station platform will hear a frequency of approximately 233.56 Hz.