- #1
Ytfeza
Hi all, is my description below a reasonable attempt in explaining how a standing wave forms?
The main part I am a bit confused as to how to explain is why the antinodes move up and down. Thanks!A standing wave is formed when energy of a wave of the right frequency is trapped in the system causing resonance to occur. This occurs when there are two progressive waves with the same frequency approaching each other in opposite directions (reflected wave superimposing with the incident wave). As the two waves superimpose there will be points in the standing wave where the two waves are always antiphase (out of phase by pi radians), so they will destructively interfere producing nodes (always nodes). In the middle of two adjacent nodes the waves will be in phase so constructively interfere to produce antinodes with max amplitude. Between a node and an antinode the amplitude varies depending on how much amplitude from the two waves constructively add together. Between two nodes the antinode's amplitude changes from max to min (up/down) as particles passes through the equilibrium position because as the two waves move their phase begins to shift, so between the two nodes constructive and destructive interference can occur. When constructive occurs the particles at the antinode are at a maximum displacement (either + or -), and when it reaches the equilibrium (same position as the stationary nodes) the two progressive waves are out phase and destructively interfere. Hence, the particles in the standing wave have the most potential energy when they are at a maximum amplitude and most kinetic when passing through the equilibrium.
The main part I am a bit confused as to how to explain is why the antinodes move up and down. Thanks!A standing wave is formed when energy of a wave of the right frequency is trapped in the system causing resonance to occur. This occurs when there are two progressive waves with the same frequency approaching each other in opposite directions (reflected wave superimposing with the incident wave). As the two waves superimpose there will be points in the standing wave where the two waves are always antiphase (out of phase by pi radians), so they will destructively interfere producing nodes (always nodes). In the middle of two adjacent nodes the waves will be in phase so constructively interfere to produce antinodes with max amplitude. Between a node and an antinode the amplitude varies depending on how much amplitude from the two waves constructively add together. Between two nodes the antinode's amplitude changes from max to min (up/down) as particles passes through the equilibrium position because as the two waves move their phase begins to shift, so between the two nodes constructive and destructive interference can occur. When constructive occurs the particles at the antinode are at a maximum displacement (either + or -), and when it reaches the equilibrium (same position as the stationary nodes) the two progressive waves are out phase and destructively interfere. Hence, the particles in the standing wave have the most potential energy when they are at a maximum amplitude and most kinetic when passing through the equilibrium.