Doppler effect: when both objects move?

[axp107]

---

Members do not see this ad.

I know there have been questions on this.. I can do these problems when 1 object is stationary.. but when they're both moving, I get confused..

Train moving at 80mph. A car in front of it is moving in the same direction at 50 mph. If freq. of whistle on train is f, what is the freq. heard by the car?

Answer:

f * ((v-50)/(v-80))

My question is, why the minus signs.. when I did the problem, I made the numerator + and denom - .. to give the largest possible value of f'

I understand that f' has to be > f, so the denominator must be less than numerator.. but why minus on top AND bottom?

I remember being taught a "systematic" way to do this... something along the lines of:

do the numerator and denom. separately.. and assume one of them is stationary..

 

[SketchLazy]

I know there have been questions on this.. I can do these problems when 1 object is stationary.. but when they're both moving, I get confused..

Train moving at 80mph. A car in front of it is moving in the same direction at 50 mph. If freq. of whistle on train is f, what is the freq. heard by the car?

Answer:

f * ((v-50)/(v-80))

My question is, why the minus signs.. when I did the problem, I made the numerator + and denom - .. to give the largest possible value of f'

I understand that f' has to be > f, so the denominator must be less than numerator.. but why minus on top AND bottom?

I remember being taught a "systematic" way to do this... something along the lines of:

do the numerator and denom. separately.. and assume one of them is stationary..

If both objects were moving towards each other, than your reasoning would be correct. But in this case, from the perspective of the car, the car is moving away from the train, while the train is moving towards the car. You are not looking to make the largest possible value of f' here. So the numerator would decrease(-) to make the frequency lower and the denominator would decrease(-) to make the frequency higher. The most important thing is to know which perspective you're using.

 

[dshnay]

I know there have been questions on this.. I can do these problems when 1 object is stationary.. but when they're both moving, I get confused..

Train moving at 80mph. A car in front of it is moving in the same direction at 50 mph. If freq. of whistle on train is f, what is the freq. heard by the car?

Answer:

f * ((v-50)/(v-80))

My question is, why the minus signs.. when I did the problem, I made the numerator + and denom - .. to give the largest possible value of f'

I understand that f' has to be > f, so the denominator must be less than numerator.. but why minus on top AND bottom?

I remember being taught a "systematic" way to do this... something along the lines of:

do the numerator and denom. separately.. and assume one of them is stationary..

Hey, here's how you do this. Seperate two systems so solve for car and train seperatley. Let's start with the car, while assuming that the train is stationary. The car is moving away from the train, thus the frequency decreases so we put - in the numerator. Now lets do the train while assuming the car is stationary. The train is moving toward the car so the freq should be heard higher by the car thus we put minus in denominator. Hope that helps.

Btw before looking at the solution i did it a little bit differently. I noticed that the change between the speeds was 30 mph thus i would be able to assume that the car is stationary while the train was moving towards the car at 30 mph. So Vo=Vs* 340/340-30. But anyways that's irrelevant since the solution is different

 

[axp107]

Aaah.. I see

so you treat them separately.. but all relative to f'

So in the denominator you put a minus, b/c freq is increasing... and to get a higher value of f' ... but in the numerator.. freq is decreasing.. so you make it so that f' is decreasing

 

[BrokenGlass]

I know there have been questions on this.. I can do these problems when 1 object is stationary.. but when they're both moving, I get confused..

Train moving at 80mph. A car in front of it is moving in the same direction at 50 mph. If freq. of whistle on train is f, what is the freq. heard by the car?

Answer:

f * ((v-50)/(v-80))

My question is, why the minus signs.. when I did the problem, I made the numerator + and denom - .. to give the largest possible value of f'

I understand that f' has to be > f, so the denominator must be less than numerator.. but why minus on top AND bottom?

I remember being taught a "systematic" way to do this... something along the lines of:

do the numerator and denom. separately.. and assume one of them is stationary..

http://forums.studentdoctor.net/showpost.php?p=4915900&postcount=806

 

[DrBowtie]

I'd just use relative. Car stationary and Train approaching at 30 MPH

 

[acurax]

I'd just use relative. Car stationary and Train approaching at 30 MPH

👍 Relative velocity is the way to go...quicker and more intuitive I think.

 

[swifteagle43]

I know there have been questions on this.. I can do these problems when 1 object is stationary.. but when they're both moving, I get confused..

Train moving at 80mph. A car in front of it is moving in the same direction at 50 mph. If freq. of whistle on train is f, what is the freq. heard by the car?

Answer:

f * ((v-50)/(v-80))

My question is, why the minus signs.. when I did the problem, I made the numerator + and denom - .. to give the largest possible value of f'

I understand that f' has to be > f, so the denominator must be less than numerator.. but why minus on top AND bottom?

I remember being taught a "systematic" way to do this... something along the lines of:

do the numerator and denom. separately.. and assume one of them is stationary..

MUCH MUCH EASIER WAY TO DO IT

if an object is moving at 80 MPH and the other object is going at 50 MPH the difference between the speed is 30 MPH toward the listener

f' = f * (V)/ (V-30)