Standing Waves are formed by the interference of two harmonic waves of the same amplitude and frequency (and therefore same wavelength), but travelling in opposite directions. Due to the interference of the two waves, there are certain points called nodes at which the total wave is zero at all times. The distance between two consecutive nodes is exactly half the wavelength. The points at the middle between consecutive nodes are called anti-nodes. At the anti-nodes the total wave oscillates with maximum amplitude, equal to twice the amplitude of each wave. Anti-nodes are also half a wavelength apart.
Question 1: Can you recognize the location of the nodes and anti-nodes in the standing wave of the figure? (Click on the graph to toggle the display between only the wave, or several superimposed waves in each period. The left buttons allow to stop the graph and to control the speed.)
Question 2: Derive an expression for the location of the nodes assuming the phases of both waves are known.
Question 3: What will be the result of the interference of two harmonic waves of the same frequency, travelling in opposite directions, but with different amplitudes? Derive an equation that explains the situation. What happens in this case with the nodes? (Click inside the A2/A1 window to change the ratio of amplitudes of two waves that form the standing wave plotted in the figure. The right buttons select the direction of the change).