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.