Calculating wave speed, frequency and wavelength

What you will learn

Use and rearrange v = fλ; SI prefixes and physical interpretation.

Specification mapping: A1.4

Prerequisites: A1.1.1

Physical principles

In one period a travelling wave advances one wavelength. Speed is therefore λ/T, and because f = 1/T this becomes v = fλ. This relation applies to periodic transverse and longitudinal waves. Use the propagation speed in the particular medium, not automatically the speed of light.

Rearrange before substituting: f = v/λ and λ = v/f. Convert kilohertz to hertz, millimetres to metres and nanometres to metres first. The dimensions confirm the equation: s⁻¹ × m = m s⁻¹. Quote answers with units and a precision justified by the input data.

At a stationary boundary, frequency is unchanged because the boundary is driven by the source oscillations. If speed decreases on entering another medium, wavelength decreases proportionally. The speed–frequency relationship is not a universal claim that raising frequency increases speed: for a given non-dispersive medium, wavelength adjusts.

Scientific diagram and interpretation

Equations and relationships

v = fλ

Worked examples and applications

Common misconceptions

Use the wave speed appropriate to the medium; sound does not travel at 3 × 10⁸ m s⁻¹.

Examination technique

Write prefix conversions explicitly before entering a calculator expression.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.