This is going to be a really complicated one so please bear with me
I'm building a Spanish guitar, and I'm making an attempt to use physics to create more projection of sound and tonal complexity within the instrument.
In a standard acoustic/Spanish guitar, when the strings are plucked, the resultant kinetic energy of vibration is transferred into the top of the guitar, and the whole top vibrates accordingly, exciting the air within the guitar, projecting the sound waves out of the soundhole on the front face of the instrument. The large internal hollow space acts as an acoustic amplifier.
However, this model is flawed, as energy from the strings is lost into surroundings, and the top transfers its kinetic energy into the back and sides, which are too thick to vibrate, and the energy is lost as thermal energy in the guitar's structure. In the average factory guitar, only 5% of the energy from the strings is transferred into sound.
I had the idea to make the guitar back very thin, and so the instrument could have two resonating diaphragms exciting the air inside the hollow space, and so increasing the efficiency of sound transfer. I did some research and it has been done, and my fears that it would make the guitar structurally unstable were disproved. However, I found myself in whole new world of problems as having two interfering sources of vibration (top and back) means that they will interfere with each other and superimpose. If the two plates are 'tuned' to have a resonant frequency that interferes constructively, it apparently creates a wonderful sounding guitar. If done so in a way that the plates interfere destructively, the soundwaves will be out of phase and 'cancel out' to create a thin, weak sounding instrument.
Herein lies my problem. The top is spruce, and the back is rosewood, which are very different densities. This is a requirement for the guitar in the way it will sound.. But it also means that for the two to match in resonant frequency to constructively interfere is incredibly challenging.
Luckily this is not all that affects resonant frequency. The top and back are braced using struts along the internal surface of the plates, which alongside the thickness of the plates can be used to control the frequency response.
Additionally, as the resonant frequency is determined by the standing waves in the plate, I could potentially use different modes of vibration (dipole, tripole) to match instead of just the fundamental resonant frequency.
I'm looking for any ideas or advice on this subject, how to use braces or Chladni patterns to match the frequencies of the top and back so they interfere constructively. I'm open to anything, it's as much an engineering as it is physics problem and there's so many people here with a lot of experience on different things, so anyone who can weigh in, I would really appreciate it.
https://goreguitars.com.au/design/#Back_Bracing This link has more info. I did email this luthier for information on the topic... he referred me to his £250 book and told me that information wasn't free. So yes, I also want to achieve this out of spite.
Thanks so much,