How are speed, period, and wavelength related in a standing wave?

Answer 1

A standing wave is "standing" still; so it has no wave velocity. L = vt; where v is the wave velocity (e.g., the velocity of the wave crest as it travels the length of the wave L in time t. When the wave is standing v = 0 because the crests, troughs, and all other parts of L remain stationary in the standing wave guide.

If the wave were not standing, we'd have L = vt so that v = L/t where L is the wavelength and t is the time it takes for a point on the wave (e.g., a crest) to travel the length L. When L is measured as one cycle (e.g., 2pi radians), we have frequency f = 1/t which is cycles per unit time (e.g., second). In which case, we call t a period. From L/t = v = Lf; so we see that, for a given velocity, wavelength and frequency must vary inversely. That is, for example, as frequency increases, wavelength has to shorten (and vice versa).