If you are more interested in the bass end of things then the Beyer mic you link to should be fine.

SOS happen to employ the services of some very knowledgeable people when it comes to speaker design so it might be worth taking a look at Phil Ward's articles in the magazine and also Andrew Goldberg's article on Monitors from earlier in the year. It is also worth searching out Philip Newell's articles on acoustics from the old Studio Sound magazine on the World Radio History website.

Can you access Audio Engineering Society papers through your university's library? If so, it would be well worth doing a search around the AES library.

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# **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

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James Perrett - Moderator
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### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

To me this throws up some queries.

Like, when you say:

Exactly how low do you want to go (what range of frequencies are you interested in)? Is it just audible musical "bass" frequencies or really low frequencies? Your paper about your Tesla coil source mentions that it can function at 1Hz; is that a frequency you're planning to measure? There are microphones which can get to well below 1Hz but they're not exactly in common use, are expensive, and require equally expensive external equipment to produce meaningful results (or to some extent simply to work at all!). They (and their companion electronics) are not things one would normally find in a music recording context.

What SPL range do you anticipate needing to record? Normal hearing range or something a bit more special in terms of high/low sensitivity? Hearing range is pretty straightforward for mics but plasma discharge units, even quite small ones, can produce pretty serious SPL and, again, transducers and matching electronics do exist which can handle above and below the range of SPLs within human hearing but, again, they come at a cost.

How accurate is "pretty accurate" and in what areas do you require accuracy? e.g. Frequency response, SPL, Impulse response?

Are you required/do you want to reference your results to any particular standard? Do the tests have to be repeatable? If so, you'll probably need a properly calibrated mic and recording chain. If it's more a case of 'all things are relative' and you're just looking to define a method to produce results which relate amongst themselves it gets a bit easier.

What aspects of the acoustical environment are you planning to analyse? Do you have an environment suitable for analysis level results at the kind of frequencies and SPL(s) you want to work with? Can you capture the information you need using a single microphone or would it need some kind of multi-element array?

Does your uni have a physics or engineering department which might be able to help you out with this kind of kit and/or facilities?

Though I might be over-thinking this :headbang:

Like, when you say:

....studying lower bass frequencies for my mathematics senior thesis... the digital input signal needs to be pretty accurate since I am doing detailed analysis of the acoustical environment

Exactly how low do you want to go (what range of frequencies are you interested in)? Is it just audible musical "bass" frequencies or really low frequencies? Your paper about your Tesla coil source mentions that it can function at 1Hz; is that a frequency you're planning to measure? There are microphones which can get to well below 1Hz but they're not exactly in common use, are expensive, and require equally expensive external equipment to produce meaningful results (or to some extent simply to work at all!). They (and their companion electronics) are not things one would normally find in a music recording context.

What SPL range do you anticipate needing to record? Normal hearing range or something a bit more special in terms of high/low sensitivity? Hearing range is pretty straightforward for mics but plasma discharge units, even quite small ones, can produce pretty serious SPL and, again, transducers and matching electronics do exist which can handle above and below the range of SPLs within human hearing but, again, they come at a cost.

How accurate is "pretty accurate" and in what areas do you require accuracy? e.g. Frequency response, SPL, Impulse response?

Are you required/do you want to reference your results to any particular standard? Do the tests have to be repeatable? If so, you'll probably need a properly calibrated mic and recording chain. If it's more a case of 'all things are relative' and you're just looking to define a method to produce results which relate amongst themselves it gets a bit easier.

What aspects of the acoustical environment are you planning to analyse? Do you have an environment suitable for analysis level results at the kind of frequencies and SPL(s) you want to work with? Can you capture the information you need using a single microphone or would it need some kind of multi-element array?

Does your uni have a physics or engineering department which might be able to help you out with this kind of kit and/or facilities?

Though I might be over-thinking this :headbang:

- forumuser840717
- Regular
**Posts:**161**Joined:**Thu Jun 16, 2016 5:20 pm

### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

Moses4525 wrote:WOW!

I need to learn a lot more about how to implement mathematics into all of this... after recording the audio produced by the Tesla coil, in your professional opinion, what would be the ideal route to take for research? I initially wanted to see how an enclosure could better the production of lower frequencies. Many hobbyist that play around with the musical tesla coils always get comments mentioning how cool it would be if there was bass. So that's my justification for wanting to implement an enclosure into the study.

I am almost positive that I will need to consult a professional to help me design an enclosure that would be useful.

Again, anyone's opinions are welcome and greatly appreciated!

If you do a quick google search for 'speaker enclosure acoustics site:.edu', you might find some results that point you in the right direction.

So tying in math - most of digital signal processing is based on the Fourier Transform - it takes a time based function and transforms it into a function of frequency. It'll be what you use to analyze the signal - you can find the magnitude (and phase) of the signal at the frequencies your'e interested in. You could devote a chapter explaining the FT in detail, starting from the continuous Fourier Transform, and then how the discrete FT is derived (for digital signals) - the latter is what you'll be using.

What's your time frame for finishing this? This semester, or the end of Spring? If you want to do something more interesting - my area of research in grad school was signal processing. My research started off in signal processing and music, and then I switched to speech processing. I have some other ideas in my head using mathematically interesting non-Fourier methods to analyze your signals.

- rockydennis
- Poster
**Posts:**11**Joined:**Sat Nov 03, 2018 6:36 am

### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

If your background is maths you might want to have a look at Mathematica as your analysis software. Mathematica is more maths oriented than Matlab. Mathematica started as a computer algebra system (although it now does a lot more), so it can e.g. give exact solutions for integrals and differential equations.

A free computer algebra system is wxMaxima.

Something that occured to me was looking at the maths of why there is no bass. I don't see a whole lot to analyse in the .wav file that will be produced. The Fourier transform will show the harmonics that come from using a stream of sparks as a sound source -- that's about it :)

A free computer algebra system is wxMaxima.

Something that occured to me was looking at the maths of why there is no bass. I don't see a whole lot to analyse in the .wav file that will be produced. The Fourier transform will show the harmonics that come from using a stream of sparks as a sound source -- that's about it :)

- merlyn
- Regular
**Posts:**149**Joined:**Thu Nov 07, 2019 3:15 am

### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

To the OP - remember that nearly all budget audio circuitry filters off frequencies outside the 20Hz to 20kHz range to avoid DC and RF and other problems. Microphones are usually not designed to reproduce infra-sound below 20Hz - indeed they are designed to reject those frequencies.

To study infra-sound I had to build my own ribbon mics using a 4" ribbon.

Looking at and measuring frequencies outside the usual 20-20 range is best done I found with an oscilloscope, as these do not have filters for obvious reasons!

What is the question you are trying to answer?

Why are you using a Tesla coil to generate sound? I am somewhat puzzled here.

But you will find a wealth of knowledge on this forum that can point you in the right direction!

To study infra-sound I had to build my own ribbon mics using a 4" ribbon.

Looking at and measuring frequencies outside the usual 20-20 range is best done I found with an oscilloscope, as these do not have filters for obvious reasons!

What is the question you are trying to answer?

Why are you using a Tesla coil to generate sound? I am somewhat puzzled here.

But you will find a wealth of knowledge on this forum that can point you in the right direction!

- The Red Bladder
- Frequent Poster (Level2)
**Posts:**2629**Joined:**Tue Jun 05, 2007 12:00 am**Location:**. . .

### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

rockydennis wrote:Moses4525 wrote:WOW!

I need to learn a lot more about how to implement mathematics into all of this... after recording the audio produced by the Tesla coil, in your professional opinion, what would be the ideal route to take for research? I initially wanted to see how an enclosure could better the production of lower frequencies. Many hobbyist that play around with the musical tesla coils always get comments mentioning how cool it would be if there was bass. So that's my justification for wanting to implement an enclosure into the study.

I am almost positive that I will need to consult a professional to help me design an enclosure that would be useful.

Again, anyone's opinions are welcome and greatly appreciated!

If you do a quick google search for 'speaker enclosure acoustics site:.edu', you might find some results that point you in the right direction.

So tying in math - most of digital signal processing is based on the Fourier Transform - it takes a time based function and transforms it into a function of frequency. It'll be what you use to analyze the signal - you can find the magnitude (and phase) of the signal at the frequencies your'e interested in. You could devote a chapter explaining the FT in detail, starting from the continuous Fourier Transform, and then how the discrete FT is derived (for digital signals) - the latter is what you'll be using.

What's your time frame for finishing this? This semester, or the end of Spring? If you want to do something more interesting - my area of research in grad school was signal processing. My research started off in signal processing and music, and then I switched to speech processing. I have some other ideas in my head using mathematically interesting non-Fourier methods to analyze your signals.

This is my last quarter of school that ends in December. So I'm honestly kid of panicking :crazy:

I learned a little bit about FT at the end of my complex analysis course that I took in the spring. I looked into the different ways I could write code to display the FT, but that's all. Could you provide a link to your research papers? or email me at wademoses@hotmail.com

It sounds like you could really help me figure out what path to take on this project!

- Moses4525
- New here
**Posts:**6**Joined:**Sat Sep 26, 2020 9:32 pm

### Re: **HELP** Mathematics Senior thesis: Acoustic study of plasma waves

merlyn wrote:If your background is maths you might want to have a look at Mathematica as your analysis software. Mathematica is more maths oriented than Matlab. Mathematica started as a computer algebra system (although it now does a lot more), so it can e.g. give exact solutions for integrals and differential equations.

A free computer algebra system is wxMaxima.

Something that occured to me was looking at the maths of why there is no bass. I don't see a whole lot to analyse in the .wav file that will be produced. The Fourier transform will show the harmonics that come from using a stream of sparks as a sound source -- that's about it :)

Awesome! Mathematica looks like a great tool for me to use!

- Moses4525
- New here
**Posts:**6**Joined:**Sat Sep 26, 2020 9:32 pm