![]() ![]() Also, change the sign of c since the wave is moving in the opposite direction. Replace λ S with λ R and v S with v R in the equation. However, λ R represents the reflected source wavelength and v R is the velocity of the reflecting object, acting as a source. The wavelength equation for a moving source and stationary observer is: Note: Although the motion is still in the positive direction, the wave is now moving in the negative direction. The object reflects the "observed" waves as if the object was a moving source. f R is the observed frequency at the moving object.v R is the constant object velocity in the x-direction.λ R is the observed wavelength of the moving object.The wavelength and frequency "observed" by the object are: Let v R be the velocity of the object, moving in the x-direction. Waves reflected off moving object Waves "observed" by moving object The observer is usually nearby the source. In this case, both the velocity of the source and observer are zero: v S = 0 and v O = 0. One method to determine the velocity of an object is to reflect a wave off the object and measure the Doppler shift caused by the motion. Start with the general frequency equation:,Īdd f Sv O and subtract f Oc from both sides of the equation: ![]() Multiply both sides of the equation by −1, factor out c, and divide by λ O Start with the general wavelength equation: Observer moving away from oncoming waves Velocity with respect to wavelength Suppose the source is stationary and the observer is moving in the x-direction from the source. Since the change is frequency is Δf = (f S − f O), the velocity of the source is: v S = − c Δ f/f O (See Derivation of Doppler Effect Frequency Equations for more information.) f S is the constant wave frequency from the source.To determine the velocity with respect to frequency, you can start with the general frequency equation: Since the change is wavelength is Δλ = (λ S − λ O), the velocity of the source is: v S = cΔλ/ λ S (See Derivation of Doppler Effect Wavelength Equations for more information.) ![]()
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