How Does Wind Affect the Doppler Effect in Jet Flight?

[ScienceGuy113]

Homework Statement

Two jet airplanes are flying due east. The leading jet is flying at 1.3 times the speed of sound. The trailing jet is flying at 464 mph (both relative to the ground). The wind is blowing 182 mph due west. If the engine of the leading jet has a frequency of 2824 Hz, what frequency is heard by the pilot of the trailing jet? The speed of sound is 607 mph at this altitude.
Answer in units of Hz.

Homework Equations

f' = f [(1+Vo/V) / (1+Vs/V)]

The Attempt at a Solution

First, I converted everything to SI units:
Jet 1: 1.3(Speed of Sound Given) = 1.3(607) = 789.1 mph = 352.759 m/s
Jet 2: 464mph = 207.427 m/s
Sound: 607mph = 271.353 m/s
Wind: 182mph = 81.361 m/s
Frequency: 2824Hz

I honestly have no idea how to incorporate wind into this problem. We've gone over similar problems in class, but they have always been under conditions where the wind speed isn't given or is "negligible."
I figured because the wind is blowing due west, the perceived "motion" of the sound waves, and because it was actually motion of the medium, I could simply add the wind speed to the speed of sound:
81.361 + 271.353 = 352.714 m/s

After doing this, I solved the problem as I would normally:

f' = 2824 [( 1 + (207.427/352.714)) / (1 + (352.759/352.714))] = 5648.36Hz

However, this is incorrect. I am almost sure I went wrong with factoring in the wind speed, but I haven't been able to find any information regarding this. Please help!

 

[anathema]

Hi there,

You are correct in thinking that the wind speed needs to be incorporated into the problem, but there are a few things you need to consider. First, the wind speed is given in mph, so you will need to convert it to meters per second in order to use it in your calculations. Secondly, since the wind is blowing due west, it will actually have a negative effect on the frequency heard by the pilot of the trailing jet. This is because the wind is moving in the opposite direction of the sound waves, causing them to travel slower and reducing the frequency heard by the pilot.

To incorporate the wind speed into the problem, you will need to use the formula you have provided, but with a few modifications. First, you will need to use the combined speed of the jet and the wind as the velocity of the medium (V) in the formula. This will give you a value of 271.353 m/s, as you have correctly calculated. Secondly, since the wind is moving in the opposite direction of the sound waves, you will need to use a negative value for the wind speed (i.e. -81.361 m/s). This will give you a final velocity of 352.714 m/s for the medium. Plugging this value into the formula, you should get a frequency of 2820 Hz, which is the correct answer.

Hope this helps! Let me know if you have any further questions.