Grade 12 Physics · The wave equation
One sentence every wave obeys
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One sentence every wave obeys

Light is a wave, and every wave — light, sound, the ripple crossing a bathtub — obeys one sentence: v=fλv = f\lambda. Read aloud: v equals f lambda. Three letters, three jobs. vv is the wave's speed, in metres per second. ff is its frequency, in hertz — how many whole waves pass a fixed point each second. λ\lambda is its wavelength, in metres — the length of one complete wave, crest to crest. That last symbol is the Greek letter lambda, said “LAM-da”. Whichever of the three the question withholds is the one you solve for.

For light in a vacuum the speed is not yours to choose: c=3.00×108 m/sc = 3.00 \times 10^8\ \mathrm{m/s}, the universe's posted limit, identical for red light, radio and gamma rays. So v=fλv = f\lambda becomes c=fλc = f\lambda, and frequency and wavelength are locked together on a see-saw: push one up and the other must come down. There is no light anywhere that breaks that trade.

Its constant companion is T=1fT = \dfrac{1}{f}T equals one over f — where TT is the period, the number of seconds one cycle takes, and ff is that same frequency in cycles per second. They are reciprocals, and the units announce it out loud: seconds per cycle against cycles per second. Neither is more fundamental; they are one fact read from either end.

Now the prefixes, because light is small and fast and the exam knows it. A nanometre is 109 m10^{-9}\ \mathrm{m}, and visible light runs from about 400 nm (violet) to 700 nm (red). A terahertz is 1012 Hz10^{12}\ \mathrm{Hz}, and that same visible band runs roughly 430 to 750 THz. Cross those bridges BEFORE the numbers enter the formula, never after — a prefix crossed late is a prefix crossed wrong.