Tuning fork frequency equation

[PainterGuy]

Hi,

I was trying to see how the frequency equation for a tuning fork is derived. It looks like it's based on the equation of cantilevered beam. In other words, I'd say that historically the equation for a tuning fork was derived somewhat in a similar fashion as was done for a cantilevered beam. Please compare the following two.

Number 1:

Source: https://en.wikipedia.org/wiki/Tuning_fork#Calculation_of_frequency

Where ρA is density per unit length and can be denoted as μ, "l" is length, and 1.875²= 3. 5156.

Number 2:

Source: https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory#Example:_Cantilevered_beam

The only difference is that "Number 1" has factor of "1/2π" but "Number 2" doesn't have it. What is the reason for it? Could you please me with it?

 

[DaveE]

f = ω/2π ? Although, I haven't studied this and I have no idea what μ is.

 

[PainterGuy]

f = ω/2π ? Although, I haven't studied this and I have no idea what μ is.

Sorry! :( It was quite obvious. I wish I could delete this thread.

 

[DaveE]

LOL, you're not the only guy that ever missed by 2π.

 

[Orthoceras]

View attachment 263430
Source: https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory#Example:_Cantilevered_beam

f = ω/2π ? Although, I haven't studied this and I have no idea what μ is.

Although definitions may be redundant for some, as PainterGuy omitted them, μ is defined in the wikipedia article as the mass per unit length, and I as the second moment of area of the beam's cross-section.