Trigonometry · Intermediate · 7 min

Anatomy of a wave

A wave has a size, a repetition rate, a horizontal shift, and a baseline. Change one at a time.

WHAT HAPPENS IF…Make a wave with amplitude 2 and period π.
Interactive exploration
Preparing your experiment…

Connect the picture to the ideay=Asin⁡(Bx+ϕ)+D,T=2π∣B∣y=A\sin(Bx+\phi)+D,\quad T=\frac{2\pi}{|B|}

The sine argument needs to change by 2π to complete a cycle. With nonzero B, that requires an x change of 2π/|B|. The amplitude is |A|.

A detail that matters

Increasing B makes the period shorter, not longer.

Keep the connection going

One idea leads to another.

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