What natural frequency would a box vibrate at if its dimensions were 60x60x100cm?

Question

If I wanted to use an enclosed wooden box 60cm x 60cm x 100cm like a speaker box, how would I work out the main natural vibrating frequency, or frequencies of that box from the size dimensions?
It’s only 1cm thick plywood.

That’s excellent info Kirchwey. Thanks.
If I wanted to make it a sealed box that resonated at it’s most natural frequency, not as a speaker, but as a sealed box that vibrates/resonates as strongly as possible at its most natural frequency,
Is there a general equation for that?
Or could a microphone be placed inside the sealed box, hit the lid, and measure it’s frequency?

Answer 1

See the ref. cited below. There are several resonant frequencies. Some are due to vibration of the box panels, and there is not enough information in your question to determine that. For application as a speaker box, you want to avoid those resonances anyway, which means using wood thicker than 1 cm (2 cm or more would be preferable) and/or adding damping material. The other resonances are due to the vibration of the air in the box. If the box is vented or ported, the dominant vibration mode is a cavity resonance which you can calculate from the "cavity resonant frequency" link in the ref. Other resonances are similar to room resonance, the natural frequency of wall to opposite wall bounce. This frequency is equal to twice the distance between walls divided by the speed of sound. However, wall bounce is undesirable as it produces a single strong peak response at resonance, whereas a ported box or "bass reflex" setup will reduce and spread out the speaker's resonant frequency, providing a smoother and deeper bass response.
EDIT (responding to your followup questions):
If I interpret you correctly, you are talking about nothing but a box, no port, no speaker. In that case you don't have the strong resonance of a ported cavity but just the weaker resonances of material plate stiffness/mass/damping and the closed-cavity (wall bounce) modes. I expect if you hit the box you are exciting the plate modes most strongly. ln other words you have sort of a percussion instrument, but with a lot of damping and without a membrane which would give it a more definite pitch as in a drum. On the other hand if you put inside the box a mike and a source of bounce mode excitation like a speaker, the mike would probably pick up the bounce modes when you tuned the speaker to drive them. Both the speaker and the mike would have to be suitably located (away from the null points of the modes) for maximum response. The second reference below discusses closed-cavity ("room") resonance in detail.

Answer 2

Another term you might want to look up is "Helmholtz resonance". Interestingly, some cathedrals used tuned cavities to help reduce the echo in the large structures. The link below offers a calculator for speaker enclosures.

Answer 3

If there's anyone answering this please also let us know, how u calculated it ??