How Does Wind Affect the Doppler Effect in a Two-Train Scenario?

AI Thread Summary
In a two-train scenario with one train emitting a 480 Hz whistle while both trains approach each other at 30.0 m/s, the effect of wind blowing at 30.0 m/s towards the whistle and away from the listener complicates the Doppler effect. The correct approach involves adjusting the velocities in the Doppler effect formula to account for the wind's influence on sound propagation. The user initially misapplied the formula by incorrectly assigning the signs to the velocities. Understanding that each speed must be considered relative to the medium (air) is crucial for accurate calculations. Clarifying these concepts will lead to the correct frequency perceived by the listener on the other train.
LeFerret
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Homework Statement


Two trains are traveling toward each other at 30.0 m/s relative to the ground. One train is blowing a whistle at 480 Hz. (a)What frequency is heard on the other train if the wind is blowing at 30.0 m/s toward the whistle and away from the listener? (assume the speed of sound is 343m/s)

Homework Equations


F'=F((V+V_d)/(V-V_d))



The Attempt at a Solution


Well the top velocity has a + and the bottom has a minus because they're going towards each other and the wind is going away from the listener and towards the source.
So I just assumed F'=480((343+30+30)/(343-30+30)) since this is the vector sum? This is wrong however and it's actually the opposite, so I need help understanding why conceptually
 
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You need to take each speed relative to the medium.
 

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