![]() The Doppler Effect equations for the change in wavelength or in frequency as a function of the velocity of the wave source and/or observer can be determined though simple and logical derivations. The derivation of the Doppler Effect equations is the most straightforward by starting with wavelength. Λ O(c − v O) = λ S(c − v S) Change in wavelength Let λ O1 be the wavelength equation for a moving source and stationary observer:įor the case when both the source and observer moving, substitute λ O1 for λ S in the When both the source and observer are moving in the x-direction, you can combine the individual equations to get a general Doppler Effect wavelength equation. Δλ = λ S/(1 − c/v O) General wavelength equation Λ O = λ S/(1 − v O/c) Change in wavelength Reciprocating both sides of the equation: In this situation, the observed wave frequency is a combination of the wave velocity and observer velocity, divided by the actual wavelength: Observer moving away from oncoming waves Finding observed wavelength ![]() Suppose the source is stationary and the observer is moving in the x-direction away from the source. Δλ = λ Sv S/c Moving observer and stationary source If the source is moving away from the observer, the sign of v S changes. Substitute this value for d into λ O = λ S − d: Observed wavelength as a function of source velocity Note: If the source was moving in the opposite direction, λ O would be lengthened. This means the wavelength reaching the observer, λ O, is shortened. When the source is moving in the x-direction, it is "catching up" to the previously emitted wave when it emits the next wavefront.
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