Determining Resonance of Rods for a Given Frequency

[Oblio]

Most of us have seen the experiment where a tuning fork that is resonating, makes another tuning fork resonant when brought close in proximity.

Theres another one where small metal rods are mounted upright with plastic knobs on top (dont know if this is necessary), and two rods of same length, etc will resonate together in the same way.

Does anyone know how, with such a rod, to determine the specifications for a rod for a certain frequency?
say for 256 hz for example, how long, thick.. etc...

Much appreciated!

 

[Danger]

I don't know the answer to your question, but I suspect that the plastic knobs are simply a visual aid. It's hard to see a rod vibrating, but it's easy to see a coloured sphere moving back and forth.

 

[sir-pinski]

To determine the specifications for a rod that will resonate at a certain frequency, you will need to use the equation for the fundamental frequency of a vibrating rod: f = (1/2L)*√(E/I), where f is the frequency, L is the length of the rod, E is the Young's modulus of the material, and I is the moment of inertia of the rod. This equation assumes that the rod is clamped at both ends and is vibrating in its fundamental mode.

To determine the length of the rod, you can rearrange the equation to solve for L: L = (1/2f)*√(E/I). You will need to know the Young's modulus and moment of inertia of the material you are using. The Young's modulus can be found in materials data tables or by testing the material in a lab. The moment of inertia can be calculated based on the cross-sectional area and shape of the rod.

The thickness of the rod may also affect its resonant frequency, as a thicker rod will have a higher moment of inertia. You can use the equation for moment of inertia (I = (1/12)*m*L^2) to determine the relationship between thickness and moment of inertia.

In the case of the two rods resonating together, they will need to have the same length and material properties in order to resonate at the same frequency. The plastic knobs on top may affect the resonance slightly, but as long as the rods are of the same material and length, they should resonate together.

I hope this helps in determining the specifications for your desired frequency. Keep in mind that there may be other factors that can affect the resonance of the rods, such as damping from the environment or imperfections in the material. It may be helpful to test and adjust the specifications in order to achieve the desired frequency.