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?

for the first part

(1/(1-(u/v)))f
1/(1-(25/343))(3000)

Instead of subtracting the (25-343) add it and you should get the correct answer. :)

To answer these questions, we can use the concept of the Doppler effect in physics. The Doppler effect refers to the change in frequency (or pitch) of a wave (such as sound or light) due to the relative motion between the source of the wave and the observer.

Let's break down the questions one by one.

1. What frequency does the boyfriend hear?
Since the train is moving towards the east, the sound waves of the whistle will be compressed, resulting in a higher frequency. This phenomenon is known as the "blue shift" in doppler effect. The formula to calculate the observed frequency (f') is given by:

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

where:
f is the emitted frequency of the whistle (3000 Hz)
v is the speed of sound in air (which is approximately 343 m/s at room temperature)
vo is the velocity of the observer (which is zero as the boyfriend is stationary on the platform)
vs is the velocity of the source (which is 25 m/s towards the east)

Plugging in the values, we can calculate the observed frequency (f'):

f' = 3000 * (343 + 0) / (343 + 25)
f' ≈ 3068 Hz

So, the boyfriend will hear a frequency of approximately 3068 Hz.

2. What frequency will the chemistry student hear before the two trains pass each other?
Since the chemistry student is on a westbound train moving towards the station, the sound waves from the physics student's train will be stretched, resulting in a lower frequency. This phenomenon is known as the "red shift" in the Doppler effect. The formula to calculate the observed frequency (f') is the same as before, but this time we consider the velocity of the source (vs) as -25 m/s (negative since it's moving towards the chemistry student):

f' = 3000 * (343 + 0) / (343 - 25)
f' ≈ 3300 Hz

Therefore, the chemistry student will hear a frequency of approximately 3300 Hz before the two trains pass each other.

3. What frequency will the chemistry student hear after his train passes the physics student's train?
After the trains pass each other, the chemistry student will now be moving away from the physics student's train. This means that the sound waves will be compressed, resulting in a higher frequency. We use the same formula as before, but this time we consider the velocity of the source (vs) as 25 m/s (positive since it's moving away from the chemistry student):

f' = 3000 * (343 + 0) / (343 + 25)
f' ≈ 3068 Hz

So, the chemistry student will hear a frequency of approximately 3068 Hz after his train passes the physics student's train.

Note: These calculations assume that the speed of sound (343 m/s) and the velocity of the trains remain constant throughout the scenario. In reality, these values can vary due to different factors, so the results might not be exact but a good approximation.