# Waves -Harmonics

#### Rockazella

I've read the definition before, but I didnt really get the significance of a harmonic. I would like to know how they are used in communication technology. Anyone know wave physics well and wouldn't mind helping me out?

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#### Tyger

Harmonics

are just multiples of a given frequency. Just like 440, 880, 1320, 1760. At least that is the usual definition. The same for both sound and electric waves.

And the notion of a harmonic goes back to the ancient Greeks such as Plato and Pythagorus.

You can learn a lot about harmonics under Fourier Series.

with regard to communications

Harmonics are generally unwelcome and efforts are made to filter them out.

#### Ivan Seeking

Staff Emeritus
Gold Member
Originally posted by Rockazella
I've read the definition before, but I didnt really get the significance of a harmonic. I would like to know how they are used in communication technology. Anyone know wave physics well and wouldn't mind helping me out?
Harmonics are the essence of the variation between of musical instruments. What is the difference between the sound of a middle C played on a piano as compared to a flute; or a guitar compared to a tuba, or to a human voice, or to a bird? To a large degree the answer is harmonics. Each instrument can produce a middle C, but each produces its own unique set of harmonics that create the characteristic sound.

Edit: just as an analog for understanding. Of course with communications, harmonics are generally bad. Note however that harmonics can be used to produce desired results also. For example, I can build an oscillator circuit tuned to the 5th harmonic of a switching device; this can effectively yield an oscillator with a frequency 5 times greater than the switching device. Also, in large industrial applications, power networks are tuned so that the harmonics between two large inductive loads will cancel.

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#### Guybrush Threepwood

Originally posted by Rockazella
I've read the definition before, but I didnt really get the significance of a harmonic. I
would like to know how they are used in communication technology.
With the help of harmonics you could do a frequency multiplier. You take a signal at n Hz, pass it through a non-linear device (...a diode) and the resulting signal has a lot of harmonics. Then filter only the one you need (let's say the one at 3n Hz). And you have a multiplier by 3...

#### Rockazella

Guybrush
what do you mean by a non-linear device? You say a diode is an example, but what makes it that?

#### Guybrush Threepwood

For example the resistor is a linear electronic device. If you make a plot that represents the current through the resistor vs. the voltage drop you get a line. This is the Ohm's law u = Ri .
If you make the same plot for a diode (called diode's characteristic) you don't get a line (look at this or this ). That's because the relation between u and i is no longer linear for the diode. Of course for some applications you can approximate the diode's characteristic as linear by working in a certain range of i, but that is not the case for the frequency multiplier.

A diode would clip an alternating signal... why would a diode set up harmonics?

#### Guybrush Threepwood

A diode would clip an alternating signal... why would a diode set up harmonics?
If you do a Fourier transform on the clipped signal, you'll get a lot of harmonics....
(http://www4.ncsu.edu/~mowat/H&M_WebSite/FFT/fft.html)
Basically any periodic signal that is not a sine wave is a sum of a fundamental sine wave an harmonics of the fundamental.

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Hey, that's a neat page!

#### Rockazella

Harmonics are the essence of the variation between of musical instruments. What is the difference between the sound of a middle C played on a piano as compared to a flute; or a guitar compared to a tuba, or to a human voice, or to a bird? To a large degree the answer is harmonics. Each instrument can produce a middle C, but each produces its own unique set of harmonics that create the characteristic sound.
How can one instrument at a given time produce a 'set' of frequencies, or harmonics?
molecules can't vibrate at more than one frequency at a given time, right?

#### Integral

Staff Emeritus
Gold Member

Lets summarize what has been said so far.

If we have some pure sine wave of frequency K it has harmonics with frequency nK, for example if K=100Hz its second harmonic is n=2 so 2K= 200Hz.. Here K is the FUNDAMENTAL each multiple is a harmonic of that wave.

It is interesting that ANY periodic waveform can be expressed as a sum of harmonic sine waves. This is called the Fourier Expansion. For example

f(x) = 4(&Sigma; Sin(n&pi;x/L)/n)/&pi;
Where the sum is over all ODD integers.
http://home.attbi.com/~rossgr1/Fourier1.PDF [Broken]
Is a graph of the fundamental, the 3rd harmonic and their sum.

http://home.attbi.com/~rossgr1/Fourier2.pdf [Broken]

http://home.attbi.com/~rossgr1/Fourier3.pdf [Broken]

This shows that high frequency content is critical to form a good square wave. If your computer does not maintain this content the square waves that are essential to the operation of your system will degrade. Computer engineers must be aware of this in order to design a successfull computer.

In communications, harmoincs are generally undesirable, they can appear as noise at some stage of amplifiction. It can be very difficult to filter out such noise as frequently your underlying signal may contain meaningful content at that frequency. This is the difficulty of audio circiutry, to accuratly reproduce and maintain fidelity of the original signal, any device that creates a sharp change in the signal (non linear) will produce high frequency harmonics. As again you must have high frequency components to create a corner.

Now as a final thought, consider your eardrum. How are you able to discern discrete instruments, or voices when it is a single small disk of tissue which is creating all the vibrations.

This question has the same answer as your question, and is related to Fourier analysis and something called the superpostion principle. (do a web search on that to see what turns up)

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#### Guybrush Threepwood

Originally posted by Rockazella
How can one instrument at a given time produce a 'set' of frequencies, or harmonics?
molecules can't vibrate at more than one frequency at a given time, right?
the four strings of mourning

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