A wave carries energy from place to place while the medium itself only oscillates about a fixed point. Describe one with a handful of quantities and a single equation ties them together: v = fλ.
A progressive wave transfers energy without transferring matter. It is described by its displacement, amplitude, wavelength, period and frequency, with phase difference comparing the motion of two points. The speed, frequency and wavelength obey v = fλ, and the intensity is proportional to the square of the amplitude.
Adjust the frequency and wavelength and watch the wave travel; the read-out confirms v = fλ at every setting. Change the amplitude and see the intensity respond as the square.
Each term has a precise meaning worth memorising.
| Quantity | Meaning |
|---|---|
| amplitude | maximum displacement from equilibrium |
| wavelength λ | distance for one complete cycle |
| period T | time for one complete cycle |
| frequency f | cycles per second, f = 1/T |
| v = fλ | the wave equation |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The wave equation relating speed, frequency and wavelength is:
A wave has a frequency of 50 Hz and a wavelength of 6.0 m. Its speed is:
Two points exactly one wavelength apart on a progressive wave have a phase difference of:
The intensity of a wave is proportional to:
The cathode-ray oscilloscope turns a signal into a picture you can measure.
Keep amplitude and intensity distinct: intensity goes as amplitude squared, so halving the amplitude quarters the intensity. When using v = fλ, make sure the wavelength is in metres and the frequency in hertz. A wave transfers energy, not matter: the particles of the medium do not travel with the wave.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A wave on a rope travels at 12 m s⁻¹ with a frequency of 4.0 Hz. Its wavelength is:
The amplitude of a wave is doubled with no other change. Its intensity becomes:
On a CRO the time-base is 2.0 ms per division and one complete cycle spans 5.0 divisions. The frequency of the signal is:
This skill is now lit gold on your star map. Keep the chain going.