b Is Not the Period

The most common slip with a squeezed wave is to read b as the period. They are opposites: b counts how many waves fit into 2π, the period is how long one wave is. Going from a graph to an equation, measure the period first, then turn it round:

b = 2pi/period

Here the tops are at π/6 and 5π/6, so the period is 5π/6 − π/6 = 2π/3. Then b = 2π ÷ 2π/3 = 3, and since the wave rises from 0 with amplitude 1 it is y = sin(3x).

Measure from one top to the next, or from one crossing going up to the next. Two crossings in a row are only half a period apart.