1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doppler Effect Compensation

  1. Jul 28, 2014 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations
    [itex]ƒ_{observed} = \frac{v}{v+v_{s}}ƒ_{source}[/itex]


    3. 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.
     
    Last edited: Jul 28, 2014
  2. jcsd
  3. Jul 28, 2014 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Check your expression for ##\theta## in terms of ##d##, ##V_s##, and ##t##. Are you sure that's what you want?
     
  4. Jul 28, 2014 #3
    Why wouldn't it be? Tan gives me opposite and adjacent components which are d and tVs. Are you saying it should be sin or cos?
     
  5. Jul 28, 2014 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Consider the sign of your expression for ##V_o## as you pass ##t=0##.
     
  6. Jul 28, 2014 #5
    Am I approaching this the right way? I don't see what else theta can be written as.

    would writing it in terms of cosine make sense? then [itex]V_{o}=\frac{V_{s}^{2}t}{\sqrt{d^{2}+V_{s}^{2}t^{2}}}[/itex]
     
    Last edited: Jul 28, 2014
  7. Jul 28, 2014 #6

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Your approach is fine, but you have to be a bit careful. Try plotting ##V_o## vs ##t##. Is it what you expect?
     
  8. Jul 28, 2014 #7
    Yes! this new Vo works. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Doppler Effect Compensation
  1. Doppler effect (Replies: 3)

  2. The Doppler Effect (Replies: 3)

Loading...