1Which of these has the same dimensions as amplitude?
Amplitude and de Broglie wavelength both have the dimensions [L].
Oscillations and wavesClass 11, Oscillations
Dimensional formula of Amplitude
[L]
The maximum displacement from the mean position. It has the dimension of length.
How to get the dimensional formula of amplitude
- Start from the definition: amplitude = length.
- Put in the dimension of each part: [L].
- Add the powers of each base quantity: [L].
Quantities with the dimensions [L]
- Length
- Displacement
- Radius of gyration
- Mean free path
- Wavelength
- Focal length
- Fringe width
- de Broglie wavelength
- Bohr radius
Equal dimensions do not make them the same quantity. Compare amplitude with the others in the full grid.
Three questions on amplitude
2What is the SI unit of amplitude?
The SI unit of amplitude is the metre (m).
3Which one has different dimensions from the others?
Frequency is [T⁻¹]. The other three are all [L].
An equation that uses amplitude
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
y = A sin(ω t - k x)y[L]=A sin(omega t - k x)[L]Dimensionally consistentEvery term is [L]
y = displacementω = angular frequencyt = timex = displacement
Amplitude: quick answers
What is the dimensional formula of amplitude?
The dimensional formula of amplitude is [L]. It comes from amplitude = length.
What is the SI unit of amplitude?
The SI unit of amplitude is the metre (m).
Which quantities have the same dimensions as amplitude?
Amplitude shares [L] with length, displacement, radius of gyration, mean free path, wavelength, focal length, fringe width, de Broglie wavelength. Equal dimensions do not make them the same quantity.