The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line, so that the source and observer are moving either directly toward or directly away from each other. If this restriction is relaxed, one must use the more general Doppler equation where θO and θS are defined in Figure P17.69a.
F - (v + vocos θ0 / v ─vS cos θ) f
(a) Show that if the observer and source are moving away from each other, the preceding equation reduces to Equation 17.13 with negative values for both vO and vS.
(b) Use the preceding equation to solve the following problem. A train moves at a constant speed of 25.0 m/s toward the intersection shown in Figure P17.69b. A car is stopped near the intersection, 30.0 m from the tracks. If the train€™s horn emits a frequency of 500 Hz, what is the frequency heard by the passengers in the car when the train is 40.0 m from the intersection? Take the speed of sound to be 343 m/s.

25.0 m/s ILI fo Vo Figure P17.69