Recall and apply: wave speed (m/s) = frequency (Hz) × wavelength (m)

The idea

This equation links three measurable wave quantities. Wave speed v is how fast a crest advances, measured in metres per second (m/s). Frequency f is the number of complete waves passing a point each second, measured in hertz (Hz), where 1 Hz = 1 wave per second. Wavelength λ is the distance from one crest to the next, measured in metres (m). Because Hz means per second, multiplying f by λ gives metres per second directly: v = f × λ. Rearranged, f = v ÷ λ and λ = v ÷ f. Example: a wave of frequency 50 Hz and wavelength 4 m travels at 50 × 4 = 200 m/s. Check units before substituting: convert centimetres to metres and kilohertz to hertz first.

What earns the marks

• Selects the relationship v = f × λ and substitutes frequency in hertz and wavelength in metres.
• Rearranges the equation correctly to f = v ÷ λ or λ = v ÷ f when the unknown is frequency or wavelength.
• Converts given values into SI units, for example 250 cm becomes 2.5 m, before calculating.
• States the answer with the correct unit, m/s for speed, Hz for frequency or m for wavelength.

Common mistakes and how to put them right

• Adds frequency and wavelength instead of multiplying them.

  Put it right: Apply v = f × λ.

• Uses wavelength in centimetres without converting.

  Put it right: Divide by 100 to obtain metres first.

• Divides by frequency when wavelength is the unknown; use λ = v ÷ f.

• Omits the unit or writes the wrong unit.

  Put it right: Attach m/s, Hz or m to match the quantity found.

Exam tips

• Write the equation, then substitute, then calculate, so a rearrangement slip is easy to spot.
• Convert every value to metres and hertz before substituting.
• Sanity-check the size: a sound wave at 340 m/s with 0.5 m wavelength should give about 680 Hz.