# Math for sound

#### thelightguy

##### Member
I am doing a book project for school about math in tech theatre. I have plenty of lighting formulas and plenty of carpenty/set stuff, but it is hard to figure out sound stuff, can anyone help?
Negative numbers are a plus. Thanks

from your other posts i gather that you are in middle school. A lot of formulas for sound involve some higher math, namely logarithms for decibels. now i don't know how advanced your math is but in anycase here is a site with some background formulas. also remember that with sound you work with electricity so i included some electrical formulas.

also check out some of the links from that site.

Thanks, that was highly informational, but as you prodicted, a bit complicated for Pre-Al. Thanks though. I appr. the responce. Google has found some stuff for me.

From all the classes I have took on sound, it involves alot of Algebra and Calc. I probably have at least 30 some equations used for sound and acoustics. Way to complicated for me.

Math for sound does get pretty complicated. I'm in calc and there are some things even I look at, smile, nod, and skip over.

However, here's some stuff you can play around with:

In sound equipment (not from a speaker), the volume level of sound is measured in decibels (dB), and the ideal level for a signal is 0 dB. Anything lower than that is a negative number, and anything higher is a positive number. Also, for every three dB increase or decrease, the volume is roughly double or half the original volume. So, a signal at -20 dB is pretty soft, while a signal at +6 dB is relatively loud.

Now, this may seem a bit odd, considering you may have heard that 40 dB is soft, and 80+ dB is loud. The reason is that sound in the air (from a speaker) is measured on a different scale, dB SPL, where 40 dB SPL relatively soft and 80+ dB SPL loud.

Des that make any sense to you? If not, I'd be happy to clarify.

also when thinking about it, there are ratios that are used in sound like the 3:1 ratio which is that for every foot a singer is from their microphone that microphone should be 3 feet from the next one, there are alot of ratios like this that are pretty simple math and you could probably get away with for your project.

while on the topic of dB, here's a fun little FYI from a light guy:

For the human ear to hear a difference in volume, you must increase the dB by 3.

So, if you are using 2 speakers and want to gain 3dB you would go to 4. then if you wanted to gain 3 dB again, you would go to 8. if you want to gain 3 dB again, then you would go to 16. Thats why at concerts, you would easily have 40 speakers per side.

Logarithms for basic Audio Math are pretty easy, if you don't go too deep into them that is. If you can understand how they work and how to use them then thats all you need to worry about unless you want to be an acoustician.

Here's some stuff that the people above skipped over that you may not know:

the term dB is a ratio. If you say +10dB, and don't give a reference then it's like saying "Dang, she's ....". As such, there are many different reference points and thats what creates the confusing array of terms (dBv, dBV, dBSPL, dBu etc...) SPL can't have a negative dB. It's bottom reference point is 0 which is the threshold of human undamaged hearing.
dBu is in reference to 0.775 volts across any load and is what is used as the dB reading in consoles and such. When the term 0dB is used on a console know that this means "same level in, same level out" as long as your eq is flat.

Here's some dB facts:
To increase a speakers SPL output by +3dB, one must double the wattage going into the speaker ie: 400watts = 101dBSPL, 800watts = 104dBSPL

To increase a speakers SPL output by +10dB, one must increase the wattage to ten times it's initial amount. 100watts=78dBSPL, 1000watts=88dBSPL

When the amplitude of a waveform is doubled, it is increased by +3dB

All these "+3 when doubled" facts are based off the 10Log formula which is as follows:

dBpower=10log(P1/P0)

there is also a 20Log formula

When you double the distance from a speaker, the dBSPL drops by 6dBSPL

dBvolts/amps/SPL=20log(P1/P0)

for both, P0 is the reference point and P1 the value after change.

Here's another formula:

MS Decode (Studio Stero Pair Bi-Directional and Cardoid Mics)
(x+y)+(x-y)=2x
(x+y)-(x-y)=2y
2x/2y=x/y
Essentially you get a stereo pair out of 3 directions and 4 inputs.

I can dig up a whole bunch more for you if you're interested. Any questions just post and either myself or another on of us sound guys'll be able to answer it

Math has invaded almost all aspects of my life!! I get confused very easily so I should probably look into a book or two about this.

for someone who has spent years arguing with math teachers that nothing past basic addition, subtraction multiplication and division and possibly simple 1 variable algebra is ever used in the real world, i am surprised to see how much math actually effects stuff when i look at all these logarithms.

Truthfully, I learned all these equations in college, but after working for an audio company for almost a year now, and even before that in my high school theatre, the only equation I've really used some division for parrallel and series connections for speakers and how it affects their impeadance.

Wait until you get to designing systems in large venues and trying to figure out coverage patterns and how speakers in different locations need to be aimed (and time/phase aligned!) to overlap in a way that creates a uniform level throughout the venue. Sines, and cosines, and tangents, oh my...sines, and cosines, and tangents, oh my...sines, and... )

geometery at the best? well at least you can you tell geometery students that you can use it in real-life.

All that sine/cosine/tangent stuff is actually trig, not geometry (although knowing that you're going to my old HS, you probably started learning it, as I did, in a class called "Geometry with Trig", unless I'm totally misremembering!).

And it's actually a combination of trigonometry and physics, since the trigonometry part is useless if you don't understand the physics of how sound level changes over both distance as you move away and angle as you move off-axis from the speaker, and how identical waves radiating from different sources interact to cancel and/or combine.

Andy_Leviss said:
Wait until you get to designing systems in large venues and trying to figure out coverage patterns and how speakers in different locations need to be aimed (and time/phase aligned!) to overlap in a way that creates a uniform level throughout the venue. Sines, and cosines, and tangents, oh my...sines, and cosines, and tangents, oh my...sines, and... )

Shhhhhh...don't tell my calculus teacher that the stuff she's teaching us actually has a use in life! Speaking of calc, isn't integration fun?! Well, it was until I had to integrate fifty million expressions for homework... ;-)

Seriously, though, I can just imagine all of the numbers people had to crunch by hand before computers aided in designing sound systems (SMAART, Ulysses, etc.)

yea andy your right, it is geo with trig, and btw i told the boss man today that you said hi. i was trying to convince him of something relating to my soundboard security issue and i thought a familiar name from among my internet sources would help lol.

digitaltec said:
while on the topic of dB, here's a fun little FYI from a light guy:

For the human ear to hear a difference in volume, you must increase the dB by 3.

So, if you are using 2 speakers and want to gain 3dB you would go to 4. then if you wanted to gain 3 dB again, you would go to 8. if you want to gain 3 dB again, then you would go to 16. Thats why at concerts, you would easily have 40 speakers per side.

Um, not so much. The reason you see so many speakers at concerts is primarily to provide even coverage, NOT more volume. Yes, more level is a function of that, and is taken into consideration, but speaker numbers and arrangement is determined so that you get the same sound level throughout an entire venue.

Each design of speaker has its own unique characteristics of how sound level changes as you move out of a direct line of it, and as you move further away. By carefully choosing patterns and aiming them right, you can get the weaker areas of more than one cabinet to add together in such a way that the overlap between two adjacent cabinets produces the same level as the direct sound of just one cabinet (this is simplifying it a bit, of course--in the real world--where compromise is a way of life--it's rarely perfect, but a good designer/tech can get a system aimed and aligned such that there's at most a few dB of difference as you walk the room).

If you don't mind some heavy reading with lots of great and clear pictures, check out Meyer's Sound Design Reference, available for \$50 from Meyer's website (http://www.meyersound.com I believe). Not the easiest read, but worth it if you're serious about working in sound at some point. And hey, maybe it could provide a good source for a project for math or physics class!

LOL, some days I wasn't sure if my name would help or hurt ) Although he's always been nice to me, and wrote me a heck of a college recommendation back then, so...

Hey I am a sophmore in highschool and am really interested in math and sound engineering and i was wondering what colleges i should look at and what classes i should be taking. I find all of this really interesting and was wondering if anyone had any good comprehesive links that could teach me some basic stuff that i'd understand (I'm taking a pre-calc honors course now). Thanks Any Rsponse Would Be Awesome!

kirbz: there is alot of math, as you've read so far involved in sound. There aren't as far as I know any specific courses in high school that cover sound in depth, though I'm sure Physics goes into it a little bit.

If you're really interested in the mathematical side of audio when you leave hs, look into acoustics depatrments. I'm sure Berklee would have a good one, if thats feasable for you.

As far as what you can do for now: make sure you have a solid grasp of algebra and are willing to learn some pretty specific physics. Then it's pretty much self study. There are alot of books around, one I read back in grade 9, way over my head, was "The Physics of Sound", the Meyer sound reference Andy mentioned is good, as is the Yamaha Sound Reingorcement Guide (I think it's published wider than meyer's and I know many professional engineers who own a copy, highly recommended.)

Hope I helped a little!