A physics student sits by the open window on a train moving at 25 m/sec towards the east. Her boyfriend is standing on the station platform, sadly watching her leave. When the train is 150 meters form the station, it emits a whistle at a frequency of 3000 Hz.

What is the frequency of does the boyfriend hear ?

A chemistry student (with nothing better to do than ride around on trains all day) is on a west bound train moving at a velocity of 25 m/sec towards the station. Before the two trains pass each other, what frequency will he hear from the train whistle from the physics student's train?

What frequency will the chemistry student hear after his train passes the physics student's train?

any one??

To answer these questions, we need to understand the concept of the Doppler effect, which describes the change in frequency of a wave (such as sound) due to the relative motion between the source of the wave and the observer.

The formula for the observed frequency (f') due to the Doppler effect is:

f' = (v ± vo) / (v ± vs) * f,

where f is the original frequency of the source, v is the speed of sound (approximately 343 m/s), vo is the velocity of the observer, and vs is the velocity of the source.

Now, let's calculate the frequencies for each scenario:

1. Frequency heard by the boyfriend standing on the platform:

The physics student is moving towards the boyfriend, so the velocity of the source (vs) is -25 m/s (negative because it is in the opposite direction). We know the original frequency (f = 3000 Hz). The velocity of the observer (vo) is 0 m/s since the boyfriend is stationary.

Plugging these values into the formula, we get:

f' = (343 + 0) / (343 - (-25)) * 3000 Hz,

Simplifying, we have:

f' = 343 / 368 * 3000 Hz,

Solving this, we find:

f' ≈ 2807 Hz.

Therefore, the boyfriend would hear a frequency of approximately 2807 Hz.

2. Frequency heard by the chemistry student before the trains pass each other:

The chemistry student is on the westbound train and the physics student's train is moving towards him with a velocity of 25 m/s. This means the velocity of the source (vs) is +25 m/s. Again, the original frequency (f) is 3000 Hz. The velocity of the observer (vo) is also +25 m/s since the chemistry student is moving with the same velocity as his train.

Applying the formula, we get:

f' = (343 + 25) / (343 - 25) * 3000 Hz,

Simplifying, we have:

f' = 368 / 318 * 3000 Hz,

Solving this, we find:

f' ≈ 3479 Hz.

Therefore, the chemistry student would hear a frequency of approximately 3479 Hz.

3. Frequency heard by the chemistry student after his train passes the physics student's train:

After the two trains pass each other, the chemistry student is now moving away from the physics student's whistle. The velocity of the source (vs) is -25 m/s. We still have the original frequency (f = 3000 Hz) and the velocity of the observer (vo) remains +25 m/s.

Using the formula once again, we get:

f' = (343 + 25) / (343 - (-25)) * 3000 Hz,

Simplifying, we have:

f' = 368 / 368 * 3000 Hz,

Solving this, we find:

f' ≈ 3000 Hz.

Therefore, after the chemistry student's train passes the physics student's train, he would hear a frequency of approximately 3000 Hz.