Waves & The Electromagnetic Spectrum
Waves
The basic equation
v = f × λ
- where:
- v = wave speed (m/s)
- f = frequency (Hz)
- λ = wavelength (m)
- The equation applies to every kind of , including sound, water ripples, and every band of the electromagnetic spectrum
- Rearrangements:
- λ = v / f (a higher-frequency wave has a shorter wavelength at fixed speed)
- f = v / λ
Common exam question
Calculating with the wave equation
Question: Calculate a wave's speed, frequency or wavelength from the other two, or show that a speed is about 3 × 10⁸ m/s (2–3 marks).
Asked in 10 of the 24 papers. Three marks are one each for substitution, rearrangement and evaluation (for a speed, one scheme credited the formula instead); two-mark versions give one for substituting or rearranging and one for the answer. One mark comes off for a power-of-ten error, so convert MHz, GHz, kHz and centimetres before you evaluate. One scheme states that a right answer with no working scores in full, and a wrong value carried from an earlier part still earns these marks. In a "show that", converting the prefix was itself a mark and the result needed two or more significant figures. Round, never truncate: one scheme rejected truncation.
A one-mark part asking for the formula often comes first: words, standard symbols and any rearrangement are accepted, with v or c for speed.
Linking frequency to period
f = 1 / T
- When a question gives you the period rather than the frequency, find f first, then use the wave equation
Worked example
Calculating frequency using the wave equation
A mobile phone transmits microwaves with a wavelength of 20 cm. Microwaves travel at 3.0 × 10⁸ m/s. Calculate the frequency of the microwaves.
Solution:
- Convert the wavelength to metres: 20 cm = 0.20 m
- Write the wave equation: v = f × λ
- Rearrange for frequency: f = v ÷ λ
- Substitute: f = 3.0 × 10⁸ ÷ 0.20
- = 1.5 × 10⁹ Hz
Leaving the wavelength in centimetres gives 1.5 × 10⁷ Hz, a power-of-ten error that costs one mark.