A traffic‐monitoring experiment is carried out on a straight
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A traffic‐monitoring experiment is carried out on a straight, flat stretch of highway. A stationary roadside sensor emits a continuous sound wave of rest frequency 16.7 kHz toward an oncoming car and records the frequency of the sound that is reflected back from the car’s front bumper. The highest frequency detected during the approach phase is 17.5 kHz. Assume still air at 20 °C and treat the car as a point reflector.
(a) Calculate the magnitude of the car’s speed and indicate whether the car is moving toward or away from the sensor at the instant the 17.5 kHz frequency is recorded.
(b) On a hotter day the air temperature rises so that the speed of sound increases to 350 m s⁻¹. Recalculate the car’s speed that would correspond to a 17.5 kHz return frequency, and determine the percent difference compared with the value from part (a).
(c) The frequency measurement has an instrumental uncertainty of ±10 Hz. Determine the resulting absolute uncertainty in the speed you reported in part (a) and express the car’s speed with appropriate significant figures and uncertainty bounds.