1Which of these has the same dimensions as intensity of a wave?
Intensity of a wave and Poynting vector both have the dimensions [M T⁻³].
Oscillations and wavesClass 11, Waves
Dimensional formula of Intensity of a wave
[M T-3]
Power passing through unit area. It has the same dimension as heat flux and the Poynting vector.
How to get the dimensional formula of intensity of a wave
- Start from the definition: intensity of a wave = power / area.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- displacement = length, so displacement is [L] = [L].
- work = force × displacement, so work is [M L T-2] × [L] = [M L2 T-2].
- power = work / time, so power is [M L2 T-2] / [T] = [M L2 T-3].
- Put in the dimension of each part: [M L2 T-3] / [L2].
- Add the powers of each base quantity: [M T-3].
Quantities with the dimensions [M T⁻³]
Equal dimensions do not make them the same quantity. Compare intensity of a wave with the others in the full grid.
Three questions on intensity of a wave
2What is the SI unit of intensity of a wave?
The SI unit of intensity of a wave is the watt per square metre (W/m²).
3Which one has different dimensions from the others?
Wavelength is [L]. The other three are all [M T⁻³].
Intensity of a wave: quick answers
What is the dimensional formula of intensity of a wave?
The dimensional formula of intensity of a wave is [M T⁻³]. It comes from intensity of a wave = power / area.
What is the SI unit of intensity of a wave?
The SI unit of intensity of a wave is the watt per square metre (W/m²).
Which quantities have the same dimensions as intensity of a wave?
Intensity of a wave shares [M T⁻³] with heat flux, solar constant, Poynting vector. Equal dimensions do not make them the same quantity.