What is the unit for resonant frequency?

Question

What is the unit for resonant frequency? where \$\omega_0 = \frac{1}{\sqrt{LC}}\$? Is it just \$HF^{-1}\$?

There is no "resonant frequency", there is only "resonance frequency": http://users.ece.gatech.edu/mleach/misc/resonance.html — Alfred Centauri, Jun 12 '13 at 01:56
@AlfredCentauri except that 'resonant' does not apply to the frequency, but to the construct which is resonating - it is the 'frequency at which the construct is resonant', as such, the 'resonant frequency [of the construct]' is perfectly valid and correct. Also, as a side note, our language evolves through the acceptance of idioms which become common usage. Try insisting that no-one calls a 'vacuum cleaner' a 'Hoover' — Matt Taylor, Jun 12 '13 at 08:11

score 11 · Accepted Answer · answered Jun 12 '13 at 00:24

11

In the simplest way possible:

L is in henries (H) - \$\Omega \cdot s\$.

C is in farads (F) - \$\dfrac{s}{\Omega}\$

Multiply both and you have \$s^2\$. Take the square root, you have \$s\$. Invert it, you have \$\dfrac{1}{s}\$, that is, \$\frac{rad}{s}\$.

If the expression is written as \$\omega_0 = \dfrac{1}{2\pi\sqrt{LC}}\$ the resonant frequency is in hertz.

answered Jun 12 '13 at 00:24

Renan

5

It's actually rad/sec, you need to add an extra factor of 2pi to get to Hz. – helloworld922 Jun 12 '13 at 00:25
yes, rad/s, thanks thats what i initially thought – azza Jun 12 '13 at 00:31
It's rad per second, but in dimensional analysis radians are the same as no unit at all because a radian is the ratio of two lengths. – The Photon Jun 12 '13 at 02:44
1

But dimensional analysis doesn't tell the whole story, it would for example let you confuse torque with energy. Also compare https://en.wikipedia.org/wiki/Steradian – starblue Jun 12 '13 at 19:43

score 2 · Answer 2 · answered Jun 12 '13 at 00:26

2

From Wiki:

\$F = \dfrac{s}{\Omega}\$ (Wikipedia entry for Farad)

Thus:

\$\dfrac{1}{ \sqrt{HF} } = \dfrac{1}{s} =\$ Hz, as expected for a frequency

answered Jun 12 '13 at 00:26

Shamtam

score 2 · Answer 3 · answered Jun 12 '13 at 02:29

\$ \omega \$ is "angular frequency" in \$ \frac{rad}{s} \$,

\$ f\$ is natural frequency AKA "frequency" in \$ Hz \$

So your title has an inherent conflict in it, you ask for frequency but talk about \$ \omega \$.

Also Radians are dimensionless so the rad in \$ \frac{rad}{s} \$ is a place holder for a scaling factor.

3 Answers3