Dimensional formula of Sound level

How to get the dimensional formula of sound level

1. Start from the definition: sound level = wave intensity / wave intensity.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. displacement = length, so displacement is [L] = [L].
6. work = force × displacement, so work is [M L T^-2] × [L] = [M L² T^-2].
7. power = work / time, so power is [M L² T^-2] / [T] = [M L² T^-3].
8. Put in the dimension of each part: [M T^-3] / [M T^-3].
9. Add the powers of each base quantity: [M⁰ L⁰ T⁰].

Quantities with the dimensions [M⁰ L⁰ T⁰]

• Angle
• Solid angle
• Coefficient of friction
• Coefficient of restitution
• Relative density
• Strain
• Poisson's ratio
• Reynolds number
• Emissivity
• Ratio of specific heats
• Relative permittivity
• Magnetic susceptibility
• Relative permeability
• Power factor
• Quality factor
• Refractive index
• Magnification

Equal dimensions do not make them the same quantity. Compare sound level with the others in the full grid.

Three questions on sound level

Related quantities

• λ Wavelength [L]
• k Wave number [L⁻¹]
• f Frequency [T⁻¹]
• ω Angular frequency [T⁻¹]
• T Time period [T]
• A Amplitude [L]