Physics
Physics
Problem
Two sound waves of frequency and equal amplitude arrive at a point with a phase difference of . Calculate the resultant amplitude of vibration at that point.Intuitive explanation
When two waves of the same frequency meet, they don't simply add their amplitudes—instead, their oscillations combine according to their phase relationship. The key is to treat each wave as a vector in the complex plane (or use the phasor diagram method), where amplitude is the length and phase is the direction. Since these waves are out of step, you'll use the law of cosines to find the magnitude of their vector sum, which gives you the resultant amplitude.
Intuitive explanation
When two waves of the same frequency meet, they don't simply add their amplitudes—instead, their oscillations combine according to their phase relationship. The key is to treat each wave as a vector in the complex plane (or use the phasor diagram method), where amplitude is the length and phase is the direction. Since these waves are out of step, you'll use the law of cosines to find the magnitude of their vector sum, which gives you the resultant amplitude.