medium difficulty5 min

Wave Speed Relation v = fλ

The wave speed relation states that speed of a wave equals frequency multiplied by wavelength, written as v = fλ.

In one line: Speed equals how often times how long each wave is.

Understand it

In the formula v = fλ, v is wave speed in metre per second, f is frequency in hertz, and λ is wavelength in metre. It is used when any two of speed, frequency, and wavelength are given. Correct unit conversion is important, especially when wavelength is given in centimetres.

Example

If sound has frequency 170 Hz and wavelength 2 m, its speed is v = 170 × 2 = 340 m/s.

Rule to remember

v = fλ, where v is speed in m/s, f is frequency in Hz, and λ is wavelength in m.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1A wave has speed 330 m/s and frequency 110 Hz.
2Using v = fλ, λ = v/f = 330/110 = 3 m.

Method you can reuse

1Write v = fλ.
2Identify given values.
3Convert wavelength to metre if needed.
4Rearrange the formula.
5Substitute values and write the unit.

Visual tip

No compulsory diagram is needed, but a labelled wave can support identification of wavelength before using the formula.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A sound wave has frequency 200 Hz and wavelength 1.5 m. What is its speed?

Think first, then show answer

The speed is 300 m/s because v = fλ = 200 × 1.5 = 300 m/s.

Common wrong answer

Λ = vf.

Why it loses marks: From v = fλ, wavelength is speed divided by frequency.

Don't mix this up

Students often forget to convert centimetres to metres before using v = fλ.

Exam tip

Write the formula first, substitute with units, and check whether the final unit is m/s, Hz, or m.