Use of formula in sound engineering

1. Oct 26, 2010

Endorser

1. The problem statement, all variables and given/known data

I realise that that the Sin and Cos graphs give wave graphs so I figure it must be related to sound engineering. Can anyone explain how? & why? this is and if it haa any application

2. Relevant equations

A sin x + B cos x = K (sin x cos φ + cos x sin φ) = K sin(x+ φ).

3. The attempt at a solution

I have tried to compare it with other equation that I have but none relate

all help is good thanks

2. Oct 26, 2010

MasterX

Yes the sin and cos functions are related to sound engineering. Look for Fourier Transformation. This transformation converts every function to a sum of sin and cos functions, where each sin and cos corresponds to a different frequency.

3. Oct 26, 2010

Endorser

Ur a Legend thanks m8

also...what would be a real life application for this function? and could you please give me an example of a transformation

4. Oct 26, 2010

MasterX

If you own a hi-fi system, then the amplifier is the best example. It is not an easy task to give an example of a transformation. The main feature of the trigonometric functions is that they are orthogonal to each other. Note, that a trigonometric function has the form Sin (n*Pi*x) or Cos (n*Pi*x), where n is an integer number. These functions are orthogonal to each other. Therefore, you have a basis, and you can use these functions to express any other function (even if it is not periodic) or to solve a differential equation.

Thus, you write

f(x)=a_0+Sum (a_n Sin(n*Pi x)+b_n Cos(n*Pi x)), where n=1,2,3,.... oo

In order to find the value of a_n and b_n you use the orthogonality property of these functions. You can truncate the above series at any number you like. But, the more terms you keep the better the accuracy would be.

The Fourier transformation is also used in the solution of the diffusion (or heat transfer) equation.

5. Oct 26, 2010

Endorser

I realise trig has the sin n cos function and n is the value that we change to find the wave but what do the values *pi*x represent and how does my inital eqaution relatet to the difussion equation in the picture attached

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6. Oct 26, 2010

MasterX

Pi=3.14...
The product Pi*x is used for spatial variation.

See here for instruction on how to solve the diffusion equation. The Fourier series naturally appear as a solution

7. Oct 26, 2010

Endorser

Spatial Variation is Changes in conditions over area.

what has this got to do with the equation and what sorts of values we put into pi*x is it frequency, magneticfield ect ect

8. Oct 26, 2010

MasterX

Pi*x and Pi*y define your domain!!
I thought that you want to do a Fourier transformation to spatial variables. Of course, you can do a Fourier transformation (FT) to time, where now you have Pi*t. If you do a FT on time then the transformed variable is frequency.

You may read this two articles: Fourier_series and Fourier_transform

9. Oct 26, 2010

Endorser

Sorry but i am not to sure what the values such as $$\sum$$ I also looked at the forum relating how The Fourier series naturally appear as a solution but are unsure what the values represent.

Sorry but could you explain more about the Pi*x and Pi*y domains. I know pi = 3.14159265358979323846... so what do we put for x in pi(x), or y in pi(y) or t in pi(t).

does the x and y represent and location? vector?
and what value we insert for t?

Last edited: Oct 26, 2010
10. Oct 26, 2010

MasterX

I do not really understand your question

The variables x (or y) are the independent variables, which denote the domain (or location, if you prefer)!
The variable t is the independent variable which denotes time

11. Oct 27, 2010

Endorser

I am thankful for your help, but I am new at all this stuff so it takes me a while to piece it all together.

now my main question is how A sin x + B cos x = K (sin x cos φ + cos x sin φ) = K sin(x+ φ) is used in sound engineering.

Now with the equation Asin(n*pi*t) + Bcos(n*pi*t)
n is the interger
pi = 3.14....
t = time ( but time of what...wave at a particular height? or time elapsed in the wave?)

know with the basic sine forumula the A and B alter the shape, length ect of graph.
So what do the A and B values do to this equation? and what purpose do they have.

12. Oct 27, 2010

MasterX

Ok, I see. I was carried away by your first question with regards to the use of trig function in sound engineering.

The equation that you have written simple states that the addition of two waves is a wave with a phase shift. Namely, if you have a sound from different sources, what you hear is one sound that is the combination of these two sounds. With the use of this equation, you can decompose this sound into each constituents.

Now, if you want to calculate the value of A and B (and you know the value of K and phi), you can use Fourier transformation. On the other hand, because this is a relative simple problem, you need to solve the following system of equations to compute the value of A and B (if you know K and phi) or compute the value of K and phi (if you know the value of A and B):

A=K cos(phi)
B=K sin(phi)

Last edited: Oct 27, 2010
13. Oct 27, 2010

Endorser

Thanks man...thats alot easier for me and I understand it better now, so let me recap

A sin x + B cos x = K sin(x+ φ)

Therefor

A = Kcosφ
B = Ksinφ
K = sqrt(A^2 + B^2)
φ = cos^-1(A/K) or sin^1 (B/K)
Regarding the X value...would that be any value from 0 - 360? cause it is a wave?

also...am I correct in saying that (AsinX) is the wave from first source and (BcosX) is the wave from the second source?

14. Oct 27, 2010

MasterX

Yes

Usually x takes value in the range -Pi, Pi, but it is OK to use 0-2*Pi
I am using Pi and 180, because x is in radians and not degrees

15. Oct 27, 2010

Endorser

ohh ok..thats simple to do

thank you very much

just 1 last thing
I have to answer a few question based on this equation, am i correct in saying

explain why we might need such a formula?

To add waves from two different wave sources together

Describe a real application of this forumla

In this case it would be used if two speakers were used, this formula would combine both the waves of the sounds and show what would be heard.

16. Oct 27, 2010

MasterX

You first answer is OK.
In your second answer replace the speakers with "sound sources". But, then again, this is not an application.
I believe that any real application is a device that plays/records music (I am not into music production, I am just guessing). Because, when you listen to a CD, you hear different instruments playing at the same time. These are different waves combined to one wave. The quality of the device is determined by its efficiency to split this wave into each constituents.

17. Oct 27, 2010

Endorser

Ahh ok... I see what you mean...I am no sound expert but it makes sence.

Thanks A hell of a lot m8...you are a great addition to physicsforums.com

thank you very much

18. Oct 27, 2010

MasterX

you are welcome