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A moving source starting at point a emits a square wave of frequency f.

Environmental Noise 183 Figure 5.25 Geometry of the Doppler Effect for Planar Motion (Seto, 1971)

If both the source and receiver are moving along the line between them then the apparent frequency is cv f' =-f (5.37)

In the case of generalized planar motion of both source and receiver, as shown in Fig. 5.25, the observed frequency is c — v cos (y — 0)

When there is a wind present with a velocity w, the frequency becomes f = c — vx + wx f (5.39)

c — ux + wx where the velocities are shown in terms of their x components for simplicity. Note that a wind has no effect on the apparent frequency unless there is also motion of the source or receiver.

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