Speed of a jet (challenging doppler effect)

[Ethan_Tab]

Homework Statement

At an air show, a fighter jet does manuevers past the crowd. Your increible hearing notes that the frequnecy of the sound coming from the jet engine drops exactly by one octave when it is approaching you to when it is directly above you (not moving relitive to you). How fast is the jet flying?

Homework Equations

Mach #= velocity/velocity sound
ƒobs=ƒo(v+-d/v+-s) where ƒo= frequency original, d= velocity of detector, s= velocity of source and v is the velocity of sound.

The Attempt at a Solution

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Since a drop by one octave is the same as half the frequency, we can represent the frequency observed when the plane approaches as ƒ and the frequency heard directly above as f/2.

we can then make two equations;
Approaching--- ƒ=ƒo(v/v-s)
Directly above--- ƒ/2=ƒo(v/v) (no s since its not moving relative to you at that exact moment)

However there are still more variables then equation, not sure how to go on from here.

 

[BvU]

Hello ET,

Scary story! jet plane overhead, not moving relative to you. Hanging from a thread ? With engine running ?

Never mind. Your notation is awful, but in $f/2 = f_0$ I see one variable disappearing, so you are left with one frequency only. Write out the equation and have a eureka moment !

 

[Ethan_Tab]

Eureka indeed.

I got the answer as being mach 0.5 for the speed of the plane. Would you concur?

 

[BvU]

The picture of a jet plane coming straight at you at half the speed of sound is also rather terrifying! Better step aside real fast !

And your answer is exactly what I got -- so either we're both right or both wrong