Wavelength

High School

Definition

It is the period of a sine wave. A period can be thought of the amount of distance over which a shape repeats its own shape. It is usually found by calculating the distance between corresponding points of the wave going through a certain phase - for example, at the troughs at of the waves.

Worked examples

\(y = \sin(x)\) has wavelength \(2\pi\)

One complete wave goes from \(x = 0\) to \(x = 2\pi\), where the pattern starts repeating.

\(y = \sin(2x)\) has wavelength \(\pi\)

The coefficient 2 compresses the wave horizontally, so it repeats twice as fast.

Measure trough to trough: \(x = \frac{\pi}{2}\) to \(x = \frac{5\pi}{2}\) gives wavelength \(2\pi\)

Distance between corresponding points in the same phase confirms the period.

Common mistakes

\(y = \sin(3x)\) has wavelength \(3\) → wavelength is \(\frac{2\pi}{3}\) Wavelength equals \(\frac{2\pi}{b}\) where b is the coefficient of x; higher b means shorter wavelength.
wavelength is the distance from peak to trough → wavelength is the distance from one peak to the next peak (or trough to trough) Peak to trough is half a wavelength, not the full repeating distance.

Where you'll use it next

You'll use wavelength when graphing and transforming trigonometric functions, solving periodic equations, and modeling waves in physics and engineering applications.

Found in 1 StudyPug lesson

Sine graph: y = sin x

Grade 12 Math

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