IGCSE Physics / Properties of waves

The wave equation v = f × λ revision notes

Edexcel International GCSE Physics (4PH1), chapter 10: Properties of waves, specification point 3.5, 3.7. Free lesson.

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The wave equation links wave speed, frequency and wavelength: v = f × λ. It applies to water, sound and electromagnetic waves, as long as you convert the values to the correct units first.

What the wave equation tells you

The equation is on the equation list, so you need to choose it and use it. Each symbol must be in the correct unit before you substitute. v is wave speed, measured in metres per second (m/s). f is frequency, measured in hertz (Hz). λ (lambda) is wavelength, measured in metres (m).

How to find wave speed

Multiply the frequency by the wavelength. The result is the speed of the wave in m/s. For example, a frequency of 0.25 Hz means one wave arrives every four seconds. If each wave is 8.0 m long, the speed is 2.0 m/s.

How to find wavelength from sound

To find wavelength, rearrange the equation to λ = v ÷ f. Convert the frequency to hertz before substituting. Kilo means 1,000, so 1.7 kHz becomes 1,700 Hz. Sound travels through air at about 340 m/s. Substitute the speed and frequency into v = f × λ first. Then divide both sides by the frequency to make λ the subject.

Convert radio frequencies before using the equation

Radio waves are electromagnetic waves. Their speed is 3 × 10⁸ m/s. Radio frequencies are often given in megahertz, so convert them to hertz before substituting. Standard form helps keep large powers of ten manageable. 1 kHz = 10³ Hz. 1 MHz = 10⁶ Hz. 1 GHz = 10⁹ Hz. For 100 MHz, multiply 100 by 10⁶ to get 1 × 10⁸ Hz.

Convert centimetres to metres

Wavelength must be in metres, not centimetres. Since 100 cm = 1 m, convert centimetres before multiplying. If you leave 5 cm as 5, the calculated speed is 100 times too large. 5 cm = 0.05 m. At 4 Hz, the correct calculation is 4 × 0.05 = 0.2 m/s, not 4 × 5 = 20 m/s.