THE DOPPLER EFFECT
You’ve probably noticed that when a car approaches you with its horn sounding, the pitch seems to drop as the car passes. This phenomenon, first described by the 19th century Austrian scientist Christian Doppler, is called the Doppler effect. When a source of sound and a listener are in motion relative to each other, the frequency of the sound heard by the listener is not the same as the source frequency. A similar effect occurs for light and radio waves; we’ll return to this later in this section.
To analyze the Doppler effect for sound, we’ll work out a relation between the frequency shift and the velocities of source and listener relative to the medium (usually air) through which the sound waves propagate. To keep things simple, we consider only the special case in which the velocities of both source and listener lie along the line joining them. Let Us and uL be the velocity components along this line for the source and the listener, respectively, relative to the medium. We choose the positive direction for both Us and uL to be the direction from the listener L to the source S. The speed of sound relative to the medium, u, is always considered positive.