A stationary orchestra tuning device emits a steady reference tone of rest frequency
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A stationary orchestra tuning device emits a steady reference tone of rest frequency f0. A second, identical device is mounted on a small cart that rolls along a straight, horizontal track toward a fixed listener at 25ms−1. At the same time, a steady wind of speed 10ms−1 blows from the moving cart toward the listener along the line joining them.
Assume the speed of sound in still air is vs=330ms−1.
(a) Taking the wind into account, derive an expression for the frequency f1 heard by the listener from the stationary source.
(b) Derive an expression for the frequency f2 heard by the listener from the source mounted on the moving cart at the given instant.
(c) Using your results from parts (a) and (b), obtain an algebraic expression for the instantaneous beat frequency fb in terms of f0, vs, the wind speed w, and the cart speed u.
(d) Evaluate fb numerically for f0=440Hz and the given wind and cart speeds. Comment on how the wind affects the beat frequency compared with a calm-air day.