Undergrad Question about finding resonant box dimensions

[needtoknow86]

Hello! I hope I'm in the right place for this questions. In short, I'm a musical instrument builder. I'm looking at placing a piece of wood above a closed resonator box. The box (also made out of wood) will have a hole in the top that is centered under the piece of wood. I know the material that I'm using as well as the frequency of the wood. How can I ensure that I build a box (needs to be a rectangle) with the proper dimensions to achieve the best resonance. I've looked at some equations, but I'm still trying to make sense of it. Thank you in advance!

 

[phinds]

Hello! I hope I'm in the right place for this questions. In short, I'm a musical instrument builder. I'm looking at placing a piece of wood above a closed resonator box. The box (also made out of wood) will have a hole in the top that is centered under the piece of wood. I know the material that I'm using as well as the frequency of the wood. How can I ensure that I build a box (needs to be a rectangle) with the proper dimensions to achieve the best resonance. I've looked at some equations, but I'm still trying to make sense of it. Thank you in advance!

If by "frequency of the wood" you mean, as I assume you do, the resonant frequency of the wood, then you can easily get the wavelength and you just need to make the box dimensions an integral multiple of the wavelength.

For example, if your wood resonates at 10Khz then you have

speed of sound = 340.29meters / second and divide that by 10,000 cycles / second and you get 3.4029 cm / cycle so you make your box dimensions 3.4029cm or 6.8058cm or ...

 

[sophiecentaur]

Hello! I hope I'm in the right place for this questions. In short, I'm a musical instrument builder. I'm looking at placing a piece of wood above a closed resonator box. The box (also made out of wood) will have a hole in the top that is centered under the piece of wood. I know the material that I'm using as well as the frequency of the wood. How can I ensure that I build a box (needs to be a rectangle) with the proper dimensions to achieve the best resonance. I've looked at some equations, but I'm still trying to make sense of it. Thank you in advance!

It strikes me that you are describing something very like a Helmoltz Resonator. the piece of wood over the hole will act like a port, although the traditional arrangement is to have a simple tube. Bass loudspeakers use the technique for lowering the natural resonance of the box dramatically. You will find a lot of Google hits about this. I found a very comprehensive one about musical instrument design which has, in Section 5, some of the basics that you can find elsewhere but it would make a good read for you. I think.

 

[needtoknow86]

Thanks for the replies! phinds, the frequency renders a wavelength of 352.04. For my project, that produces a box that is too tall... in that case, if I reduce the height, does length and width come into play? Or at that point, am I just settling for less resonance? Is there a way to find a cubic measurement that best works with the frequency that I'm dealing with, essentially allowing me to mess around with height, length and width to match the frequency I have. Thanks for the read, sophiecentaur! I'll probably have some questions about that. This kind of stuff fascinates me, thanks again!

 

[needtoknow86]

Hello again, I found an equation that looks like it might help me with my problem. In the attached .pdf It's the first equation on page 3. I understand everything except for the authors use of p, q, and r, in which he states that they're integer that are respectively associated with the dimensions. He later gives a chart indicating using a variety of 0's, 1's, 2's, etc. in order to solve the equation. Are p, q, and r simply chosen to satisfy the equation or is there some logic to what they need to be? I hope I'm explaining everything alright. I apologize as I'm sure some of you are shaking your head at my lack of vocabulary and understanding of the subject! Anyways, thanks again in advance!