A stationary observer stands at the origin of an -coordinate system
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A stationary observer stands at the origin of an xy-coordinate system. A race car travels in a straight line parallel to the y-axis along the line x=200m, moving northward (toward +y) with a constant speed of 60m⋅s−1. The car’s horn emits a tone whose rest frequency is 400Hz. Neglect wind.
(a) Calculate the frequency heard by the observer at the instant the car passes the point with coordinates (200m,0).
(b) Derive an expression for the frequency detected by the observer as a function of the car’s y-coordinate. Then determine the frequency when the car is at (200m,300m).
(c) Describe qualitatively how the detected frequency changes as the car moves from far south of the observer to far north of the observer, citing any extrema or symmetry in your expression from part (b).