Question on a doppler effect problem and equation

AI Thread Summary
Two trains are approaching each other, with Train #1 moving at 130 km/hr and Train #2 at 90 km/hr, while Train #2 emits a horn at 500 Hz. The challenge lies in determining the frequency heard by the engineer on Train #1, as both trains are in motion. The relevant equations for the Doppler effect must be adapted since both the source and observer are moving. The correct formula to use is f_o = f_s (v ± v_o) / (v ± v_s), where the signs depend on the direction of motion. The engineer needs to apply this formula correctly to find the observed frequency.
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Homework Statement


Question: Two trains on separate tracks move toward one another. Train #1 has a speed of 130 km/hr and train #2 a speed of 90km/hr. Train 2 blows its horn, emitting a frequency of 500 Hz. What frequency is heard by the engineer on train #1?


Homework Equations


This is where I get stuck. Because this is a problem where two objects are moving towards each other their is no set equation according to my teacher. You have to "make one up" depending on the problem. So here are the equations I know.

Source is moving and the observer is stationary:
fo=fs(v/v-vs) For a source moving toward stationary observer. frequency goes up
fo=fs(v/v+vs) For a source moving away from a stationary observer. frequency goes down

Source is stationary and the observer is moving:
fo=fs(1-vo/v) For a source moving away from a stationary source. frequency goes down
fo=fs(1+vo/v) For a source moving toward a stationary source. frequency goes up

I don't understand how to get equations for a problem where both objects are moving from these equations above.


The Attempt at a Solution


First I converted 130km/hr to m/s and got 36.1m/s. I did the same with the 90km/hr and got 25m/s.
Vo=36.1m/s
Vs=25m/s
Fs=500Hz
v=331
Fo(train #1)=?

I know all the terms I just don't know what equation to use.
 
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In these situations, this equation can be applied (proof might be a bit tricky though):

f_{o}= f_{s} \large \frac{v \pm v_{o}}{v \pm v_{s}}

Where you would choose the signs of the basis of the convention you mentioned. For example, in your case, the numerator would be plus, and the denominator minus.
 
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