Question

A train is moving parallel and adjacent to a
highway with a constant speed of 22 m/s. A
car, at time t0, is 21.5 m behind the train,
traveling in the same direction as the train
at 43 m/s, and accelerating at 5 m/s2. The
train’s whistle blows at a frequency 430 Hz.
At the moment t0, the car’s driver hears a
whistle from the train.
What frequency does the car’s driver hear?
The speed of sound in air is 343 m/s.
Answer in units of Hz

Answer 1

First, the acceleration and the distance between the train and the car are irrelevant. The equation you want to use is as follows:\[f _{O}=\frac{ (v \pm v _{O} )}{ (v \pm v _{S}) }f _{S}\]
where v is the velocity of sound in the medium; vO is the velocity of the observer; vS is the velocity of the source; fS is the frequency emitted by the source; and fO is the frequency heard by the observer. Now if the observer is moving toward the source, vO is positive. If the observer is moving away from the source, vO is negative. If the source is moving away from the observer, vS is negative. If the source is moving toward the observer, vS is positive.

Answer 2

At a time t, after the car has passed the train
and is a distance 11.5 m ahead of the train, the whistle blows again.
What frequency does the driver hear?
Answer in units of Hz

I got the first part of the question thank you @PsiSquared
however I tried using the same equation for the second part and I got it wrong. Would I have to use the distance for this part?

Answer 3

No, distance has no bearing on the problem. The same equation is used; however, the signs on vS and vO have changed. The observer is now moving away from the source, but the source is still moving in the direction of the observer. So now, using the appropriate signs, we get the following equation:\[f _{O}=\frac{ (c-v _{O}) }{ (c-v _{S} )}f _{S}\]It can be a bit confusing sorting out the signs in the equation. I remember the signs like this:

1. If the observer's motion vector points at the source, then vO is positive. If the observer's motion vector points away from the source, vO is negative.

2. If the source's motion vector points at the observer, vS is negative. If the source's motion vector points toward the observer, vS is positive.

I've drawn the two different problems and the associated motion vectors in the attached jpeg. In the drawings, S is the source, and O is the observer.

Answer 4

Does that help?

Answer 5

I got 401.869 Hz but I used 343 m/s as "c" and for some reason I got the answer incorrect, I may have done math wrong but I'm not sure. However, I thank you for you help and introducing me to the correct equation.

Answer 6

What is the answer supposed to be?

Answer 7

I don't know its an online assignment and they give us 7 chances to get the answer correct but they don't give us the answers