Calculating frequencies with the Doppler Effect

[Luke Frederiks]

Homework Statement

A train moves at a constant speed of v = 25.0 m/s toward the intersection shown in Figure P13.71b. A car is stopped near the crossing, 30.0 m from the tracks. The train’s horn emits a frequency of 500 Hz when the train is 40.0 m from the intersection. (a) What is the frequency heard by the passengers in the car? (b) If the train emits this sound continuously and the car is stationary at this position long before the train arrives until long after it leaves, what range of frequencies do passengers in the car hear? (c) Suppose the car is foolishly trying to beat the train to the intersection and is traveling at 40.0 m/s toward the tracks. When the car is 30.0 m from the tracks and the train is 40.0 m from the intersection, what is the frequency heard by the passengers in the car now?

Figure 13.71b: http://i.imgur.com/b08nVys.jpg

Homework Equations

[/B]
The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line so that the source and observer are moving either directly toward or directly away from each other. If this restriction is relaxed, one must use the more general Doppler equation

f ' = ((v + vi cos θi) / (v − vs cos θs))*f

where θi and θs are defined in Figure P13.71a. Use the preceding equation to solve the following problem.

I find the whole concept of Doppler effect in physics to be rather complicated. I would not only love to understand this problem but the concept in general. Any help would be appreciated.

 

[berkeman]

Homework Statement

A train moves at a constant speed of v = 25.0 m/s toward the intersection shown in Figure P13.71b. A car is stopped near the crossing, 30.0 m from the tracks. The train’s horn emits a frequency of 500 Hz when the train is 40.0 m from the intersection. (a) What is the frequency heard by the passengers in the car? (b) If the train emits this sound continuously and the car is stationary at this position long before the train arrives until long after it leaves, what range of frequencies do passengers in the car hear? (c) Suppose the car is foolishly trying to beat the train to the intersection and is traveling at 40.0 m/s toward the tracks. When the car is 30.0 m from the tracks and the train is 40.0 m from the intersection, what is the frequency heard by the passengers in the car now?

Figure 13.71b: http://i.imgur.com/b08nVys.jpg

Homework Equations

[/B]
The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line so that the source and observer are moving either directly toward or directly away from each other. If this restriction is relaxed, one must use the more general Doppler equation

f ' = ((v + vi cos θi) / (v − vs cos θs))*f

where θi and θs are defined in Figure P13.71a. Use the preceding equation to solve the following problem.

I find the whole concept of Doppler effect in physics to be rather complicated. I would not only love to understand this problem but the concept in general. Any help would be appreciated.

Welcome to the PF.

The Doppler effect is pretty straightforward and intuitive, IMO. Can you post links to some of the reading you have been doing about it, and ask specific questions about anything that is confusing you?

It looks like the main twist in this problem is the fact that both the train and car are moving -- how do you think you should handle that part?