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bwinter
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Homework Statement
Trying to find the formula to generate a sin wave that would compensate for the Doppler effect if played from a car moving 50 mph past a stationary observer 1 meter from the car's path.
Homework Equations
[itex]ƒ_{observed} = \frac{v}{v+v_{s}}ƒ_{source}[/itex]
The Attempt at a Solution
Tried to work this out using variables first. Say d is the distance from observer to car's path.
First, we want to keep the observed frequency constant, so rewrite Doppler formula for source:
[itex]ƒ_{source} = \frac{v+v_{s}}{v}ƒ_{observed}[/itex]
Then, taking the component of the car's velocity towards the observer
[itex]V_{o} = V_{s}cosθ[/itex]
Where θ is the angle between the car's path, and the direct line of sight to the observer.
But we want this in terms of d, time t and Vs, so we can rewrite θ thusly
[itex]θ=tan^{-1}(\frac{d}{V_{s}t})[/itex]
And then plugging back into Vo, we get
[itex]V_{o}=\frac{V_{s}}{\sqrt{(\frac{d}{V_{s}t})^{2}+1}}[/itex]
So plug this back into our Doppler equation.
[itex]ƒ_{s}=\frac{v+\frac{V_{s}}{\sqrt{(\frac{d}{V_{s}t})^{2}+1}}}{v}ƒ_{o}[/itex]
I've tried graphing this using ƒobserved=440 Hz and Vs=22 m/s, and the graph is symmetrical about t = 0, when it obviously should not be. I'm not sure where I'm going wrong.
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