Vibrations and Waves · Problem 2-3
The free vibrations of physical systems — A.P. French
Physics — Waves · beats-superposition
Problem
Two vibrations along the same line are described by the equations Find the beat period, and draw a careful sketch of the resultant disturbance over one beat period.Intuitive explanation
When two waves with slightly different frequencies overlap, they create a slow modulation pattern called beats—the amplitude grows and shrinks periodically. The key insight is that the beat frequency equals the difference between the two frequencies, and the beat period is simply the reciprocal of that difference. Sketch the resultant by recognizing it as a rapid oscillation (average of the two frequencies) whose envelope (amplitude) varies slowly at the beat frequency.
Intuitive explanation
When two waves with slightly different frequencies overlap, they create a slow modulation pattern called beats—the amplitude grows and shrinks periodically. The key insight is that the beat frequency equals the difference between the two frequencies, and the beat period is simply the reciprocal of that difference. Sketch the resultant by recognizing it as a rapid oscillation (average of the two frequencies) whose envelope (amplitude) varies slowly at the beat frequency.