Sound waves is a form of energy that can be measure my Hertz (a frequency measure).

What happens wen two sounds were produced at the same time. Lets say one at 440hz and the other at 220hz. What is the resulting sound in hertz?

they interpolate each other... and we call them "beat"

e.g. a very very similar frequency say 110hz and 111hz

another parameter also come into play... magnitude

it is the timing of the frequency that determine the magnitude

say,

frequency A at 60Hz so, it osccillate oen time every 1/60second... with maximum magnitude of 10dBa

frequency B at 61hz which osccilate at 1/61second per one cycle with magnitude of 10dBa as well....

so, B is faster than A...

when the time is 10 second, A has reach 1/6 time of its magnitude say.. 1.6666666666.....

same for B at 10 second with magnitude of 1.6393443dBa

the two wave travelling at different speed and SO, there will be time where one is at +ve and the other is -ve


as for this 10 second case, both is at positive, so the total magnitude is A + B at 10 second interval....

it is the totally identical Hz with the natural Hz that we known as resonance

This post has been edited by Awakened_Angel: Sep 14 2010, 02:10 PM

Thank you. Being an engineer, you have given a scientific answer. Unfortunately, I do not have a good background in science. I only understood
I am specifically looking at it from a music point of view. I am trying to get the computer to play a tune by sending a certain frequency to the speaker. For example, the note Do (261.626hz) and the note Re (293.665hz) were to be played simultaneously, what is the resulting frequency?

refer to the links



from the simple eg that ai worked out, it is seen that resultant is that the magnitude reach 0 when t=5sec which mean, t(resultant) take 10sec for one full cycle

so, you have it.. 10sec for one cycle

so, the frequency is 1/10 Hz

(I just agak agak put the numbers only, might not be accurate & not making any sense at all )

it is the same...

to get the total resultant, you need to work out the two frequency so they interpolate with each other

take this laymen example:

A person.. small girl
B person... adult male

both of them scream at the same time standing side by side at totally different magnitude(loudness) and frequency

there aretiems where the adult`s voice would be louder or lesser than nromal.. due to the girl`s voice amplify or neutralise the magnitude due to interpolating of both wave



This post has been edited by Awakened_Angel: Sep 14 2010, 03:03 PM

Good example. Comparing one with another twice as fast. 20hz move 1 cycle while 10hz only move half.

Given that you did tA + tB, "Interpolate" is also the same as saying "horizontal summation"?

You are giving me an answer in magnitude measure by dBa (as written by your y axis). I was looking for an answer in hertz.

I guess if you sum f(A) and f(b) horizontally you will get another function say f(d) which I think you plotted two points (one point being an estimate). As it is, I should be able to obtain f(d) and eventually work out how many hertz, right?

This dBa which I guess is a measure of volume? While I can understand volume = 0 (meaning no noise), I am not sure what negative volume means.

Do they really ossilate up and down the zero?

This post has been edited by faceless: Sep 15 2010, 12:10 PM

where you come out with this?



you can calculate the F from the graph after you interpolate the resultant

wrong concept... direct summation does not yield the accurate result



what is sound? Sound is define as molecular`s vibration that is detectable by human ear.... the dBa is the intensity on how strong the thing vibrate/osccilate

not quite... take this simple example...

take a ruler... hold it with your hand and left the other half in open air.. now, use your other hand to hit the free end. It will swing right? up, center, down again and again.. until the energy that you apply are used to fight the plasticity of the ruler & against air resistance/drag

now, when that ruler swing, it distort the air around you(same goes to speaker) and alas, our mortal ear could not pickup this wave at all frequency at all magnitude....

as for the ruler, it swing up and down, when it is up, we consider it as +ve and down as -ve while center as 0

P/S here`s another simple test

apparatus: 2 human, 1 rope
method: each human hold the rope at each end, both would swing the rope at different speed & power(magnitude)

result.. see for yourself

This post has been edited by Awakened_Angel: Sep 15 2010, 02:09 PM

Horizontal Summation
I am not sure where I got this term from. School had been ages ago. It is most likely from math. Since a practising engineer have not heard such term before then lets just say I learnt math from the eskimos.

Let me see if it is the same as interpolating. We will take an easier example. Graph 1 is y = x^2 (^ means to the power of in this case y=x squared). Graph 2 is y = 50. If you interpolate both the graphs would you get y = x^2 + 50?

close.....

Now can you tell me given a frequency and magnitute how do I get the above graphs?

it is an idealised motion. Such constant, uninterupted graph is hard to obtain in the real world

Then tell me how to a get an ideallised motion?

read me.. you will NEVER get it. IF you can get it, it wont be known as IDEALised

what you can do is to get closer and closer to it

P/S it is like you ask me. what is my Ideal Wife? sure is pretty, perfect body shape, fine complexion, knows how to cook, knows how to dress nicely, considerate, manja manja with you, good on bed , what else?

and you ask me, how to find this woman? I also want to know...



This post has been edited by Awakened_Angel: Sep 20 2010, 03:29 PM

As I mentioned previously, I was trying to apply it to music. You play two or more notes simultaneously its call a chord. Electronic keyboard seems to be able to do this just fine. I am sure there is a way. It comes down to - do we know how or not.

Thanks for your input, Awakened.

It is called convolution, it is pretty nasty stuff if you are not familiar with the mathematics involved. Though what is posted above is a graphical way of doing it but not practical. This site may assist in understanding how it works better http://www.jhu.edu/signals/convolve/

That is why we deal with these things as frequency components. Have you heard of the frequency spectrum?

EDIT: for that applet, y(t) is the resultant wave we 'hear', also the resultant of the convolution. Alternatively you can use the applet here http://www.jhu.edu/signals/listen-new/listen-newindex.htm under harmonic contribution, simply click at the magnitude spectrum to add a frequency together and hear what it sounds like, you'll get the idea.

This post has been edited by befitozi: Sep 20 2010, 07:59 PM

You are giving heavy stuff la.. hard to digest

That's what the applets are for =D

P/S I have all returned my mathematics to my lecturers.... after 5 years into business, I only left with the theory & formulae.... compared to tedious & complicated mathematical solving skills....

Thanks Befitozi,
As long as the answer is in term of hertz, it is the answer that I seek. I am not able to see the pictures/applets. Reading the text, I gather that it is actually looking for the area between the graphs since intergal calculas was used.

I have not heard of the frequency sprectrum. I just look it up on wikipedia. It just apply the light spectrum (a form of wave) to sound (another form of wave). It also give me links to look up the math I did not learn (like Fourier Transformation).

Looks like more reading for me. When all is done, I wonder if I could get vb (the programming I use to do this project) to do integrate a cosine wave.

Awakened,
Dont feel so bad and apologetic. The graphs you done at the beginning had put the science in a math form. In that from presentation, it had help me undertand the concept of sound waves much better.

Heavy math stuff is not a problem. No matter how a number is transformed into another number it can usually be traced back to plus and minus. From there you go to divide and multiply and subsequently to exponentials ... Heavy science stuff is a problem because I did not go to science streem. I lack the knowledge of the fundamentals to move from concept A to Concept Z.

if this is true, and you comprehend what I meant, then you are a talented science minded person indeed

I have done some homework and I am stuck.

These stuff are base on the second link Befitozi provided
A pure tone can be written as a cosinusoidal signal of amplitude , frequency , and phase angle. Frequency in units of radians/second, with t in seconds, and the phase angle to be in radians.

An alternative is to express the frequency in units of Hertz, abbreviated Hz, given by f1 = Freq/2pi

I think this 2pi is a radian measure. Convert to degree it should be 180 degrees?

In the Fourier series these frequecies are added up. The result is a list of constants that add up to a bigger constant. I wonder about appllying intregration to it.

you are right.... it is just different unit for same measurement... feet vs meter vs yard ; pound vs kg ; gallon vs litres

radian is a unit used specifically for some application in engineerings..... as it is easier to use radian than degree in some part

Converting 2pi to degrees is 360 degrees, thus forming a complete circle or in this case,a complete period.

The frequencies are not added up,it is the complete sinusoid is added up. The expression where you see terms of cos are added up is as simple as it gets bar simplifying it into a summation term. Though it must be of harmonic signals only, as so Fourier series is defined as such.

Integration would bring this into the realm of Fourier Transform which converts signals from the time domain to the frequency domain. In terms of musical notes, it is not necessary since the notes are already defined in frequency.

I could go to great lengths on this directly related to music notes when i progress into my 3rd and 4th year of my engineering course. Looking at this field particularly. Developing a device where an input music file (mp3) would output a music score sounds interesting Though it is severely limited hahaha, for undergraduates at least

English** dude.. english**.... luckily I dwelled in the never land of engineerica... and manage to speak a phrase or two in ENGLISH*

** England`s mother tongue....

*ENGINEERING`s mother tongue... math

It's just mixing two signals together. The resultant is a waveform where the spectrum consist of 220Hz. and 440Hz.

This post has been edited by Drian: Oct 6 2010, 12:22 AM

I think I get this. Circumference is 2 x pi x radius. Since the largest sin or cos value is 1, the radius must be 1 (that much I gathered from a doing math revision recently through online tutorials). Thus it becomes 2pi. Tell me if I am correct?

I am not sure I get this part correctly. Let me tell you my simplistic view about it. From the given link, tone = Amplitude x cos(frequency in radian + phase angle in radians). If the whole thing is express as Hertz then it may be as simple as say 440/2pi hertz. Lets say the entire thing in bold is written as X. In a Fourier series I can write x(t) = x1+x2+x3+...+xn. Then again x can also be written as k/2pi (a constant). Thus adding the string of x is also a constant.

I am not commenting on you third paragraph. I think I need to understand the second paragraph first. I am not dealing with mp3. I am sending a frequency to the computer speaker to play a sound. It does not require sound card. I think mp3 stuff needs a sound card.


Drian, I dont get what you are trying to say.

This post has been edited by faceless: Oct 6 2010, 09:31 AM

The question is what is the resulting sound in hertz. So my answer is there is no resulting sound in hertz.
The sounds will mix together to form a waveform with no specific frequency. However if you were to do a fourier transform to ge the spectral analysis, you'll find the 220Hz and 440 Hz

Thanks Drain,
I beleive Awakend covered what you have said in the earlier parts of this thread. In summary it was basically like - at times 400Hz will drown out out the sound of 220Hz and at other times the other way around.

For that I pose you the same question. What is the frequency chosen by eletronic keyboards manufacturers when more than one note is pressed?

Again there's no "frequency" chosen. The just mix both notes digitally and output the resultant waveform through the speaker.The resultant waveform has no particular frequency. I don't know why you keep on thinking that the resultant waveform must have some form of frequency. Any mp3 song consist of thousands of frequencies mix together, but the song itself has no particular frequency.

There is no resultant frequency only if the by product is not a sin or cos wave. If the by product, like through convolution, give another sine wave there is a frequency. That so far had been my understandng base on material given to me here. Are you telling me the resultant is not a sine or cos wave?

Yes the resultant is not a sine or cos wave. It's just a waveform.
Also to be exact an electronic keyboard does not produce sine wave. They produce a tone with a certain spectrum for each note. So a note might contain a certain range of frequency component. There's no single 220Hz or 440 Hz when you play any note. It's a range of frequency with the dominant frequency at a certain frequency. If that was the case , all instruments will sound the same.


You should try reading this
http://eamusic.dartmouth.edu/~book/MATCpag..._sum_sines.html

This post has been edited by Drian: Oct 6 2010, 03:30 PM

Thanks for the link Drian,

I did come across another link that simply say take the average of both frequency as the resultant frequency. I extracted part of it and paste it here. I have also included the link if you want to read the entire passage. What are your comments.


For example, if you add a wave oscillating at 445 Hz with one that is at 450 Hz, the resulting frequency will be an average of the sum of the two waves: (445 Hz + 450 Hz)/2 = 447.5 Hz. This waveform is close to a sine wave, since the frequencies are almost the same.
The amplitude of volume of this combination will oscillate at the beat frequency of the difference between the two: (450 Hz - 445 Hz) = 5 Hz.
Now, if you add 440 Hz and 500 Hz notes, the resulting waveform will be a complex version of a sine wave and will sound like a blurred or fuzzy average of the two tones. The average frequency of this complex wave will be (440 Hz + 500 Hz)/2 = 470 Hz.
Also, its beat frequency will be 60 Hz, which would sound like a very low-pitched hum instead of a fluctuating volume.

http://www.school-for-champions.com/science/sound_beat.htm

Befitozi & Awakened, I appreciated your comments too.