Wavelength, Frequency, Period, and Speed

A wave has one speed, set by the medium it moves through. Sound in room-temperature air always moves at about 343 m/s, no matter what pitch you play. That speed links two other properties: frequency, how many wiggles pass a point each second, and wavelength, the physical length of one full wiggle. The relationship is v = f x wavelength. Since v is locked by the medium, f and wavelength are stuck in a seesaw: push frequency up and wavelength must shrink, so their product stays equal to v.

The same wave looks different depending on how you look at it. Freeze time and take a snapshot along space, and you see wavelength: the distance from one crest to the next. Stand still at one point and watch time pass, and you see period: the time for one full crest-to-crest cycle to go by. Frequency is just 1/period, the number of cycles per second. Wavelength is a spatial ruler; period is a time ruler. Both describe the same repeating pattern, just sliced along different axes, and the wave's speed is what converts one into the other.

This idea is the toolkit for everything else in the unit. Interference, standing waves, and diffraction patterns all depend on comparing a wavelength to some physical size, like a slit width or a string length. Before any of that math works, you need to be fluent in swapping between f, T, wavelength, and v, since every fringe-spacing and resonance formula downstream is built on v = f x wavelength.