Example 1. A car moving at a velocity 50 mi/hr~ 22 m/sec is passing a stationary sound source that emits a frequency 500 Hz (Figure 8.4). The closest distance between source and the car is 20 m. Find the apparent frequency heard by the driver as a function of the distance x. Assume cs = 340 m/sec. Figure 8.4. Example 1. Observer moving along a line not intersecting the source. In this case, the velocity of the car is not directed directly toward the sound source, and we have to find the component of the velocity vector that is directed toward the source (Figure 8.5). It is given by Figure 8.5. The velocity complement toward (or away from) the source is responsible for the Doppler shift. u0 cos u0 x x 20 2 2 22 x x 202 2 m sec, where we have converted the velocity of 50 mi/hr into 22 m/sec. Then the apparent (Doppler-shifted) frequency is cs u0 cos cs 22 x 500 1 2 Hz. 2 340 x 20 v x v0 You should plot this as a function of x for 100 x 100 m. At x = 0, the car is moving purely perpendicular to the wave and at the instant when the car passes this point, the driver hears the true frequency, 500 Hz.