# How to determine harmony frequency in sound?

1. Dec 15, 2011

### oem7110

If a sound frequency is given at 1800Hz, how can I determine what range of low frequency would create a harmonic or non-harmonic (which is opposite with harmonic) vibration with 1800Hz?
Thanks in advance for any suggestions

Last edited: Dec 15, 2011
2. Dec 16, 2011

### schip666!

Any integer multiple, or divisor, should give you a "harmonic". Usually small integers. If you are talking music, the 7th harmonic is considered rather unpleasant so it's often the dividing line between good sounding harmonics and all the rest...

3. Dec 16, 2011

### oem7110

If the divisor is 18Hz, 1800Hz/18Hz = 100, which returns the remainder after division equal to 0, will it be in harmonic? in term of physics, what would it be changed on sound property for 1800 Hz?

On the other hands,
If the divisor is 7Hz, 1800Hz/7Hz = 257.142, which returns the remainder after division does not equal to 0, will it be in non-harmonic? in term of physics, what would it be changed on sound property for 1800 Hz?

Thanks you very much for any suggestions

4. Dec 17, 2011

### DaveC49

An harmonic relationship exists whenever one frequency is an integer multiple of another frequency f2=n*f1 where f1 is the lower frequency. The biological effect of harmony comes about through resonance where the detector ( eg cilia in the ear canal) has a natural fundamental frequency but responds to higher integer multiples of this frequency). In a 1D case, this can be envisaged as the wavelength of 1 cycle corresponding to the physical dimension of the object, at the second harmonic, two cycles corresponding to the physical dimension, etc. The velocity of a wave v and its frequency, f and wavelength, λ in any medium are related by v=fλ. The wavelength is the distance travelled by the wave in the period T=1/f at the velocity v. Resonances occur for an object of dimension d whenever nλ=d for some integer n, and absorption of energy by the structure from an incident wave at a given f or λ is usually largest when there is a resonance.

5. Dec 17, 2011

### sophiecentaur

I don't know what you mean by "non-harmonic" but any frequency that results from dividing your start frequency (1800Hz) by an integer can produce a harmonic at 1800Hz. In most circumstances, it is only low order harmonics that are created to any significant level - so it would be unlikely to produce 1800Hz as the 100th harmonic of 18Hz! Low order harmonics (up to, say, the seventh, are often present in naturally oscillating structures (like musical instruments) although it has to be said that most 'physical' oscillators tend to have 'overtones' that are not exact harmonics of the fundamental. The reason for this is that the natural resonance depends upon the formation of standing waves and there is nearly an 'end effect' which alters the effective length of, say, of a wind instrument according to the particular overtone that is involved. Although we usually talk of harmonics (and the harmonic content will affect the tone of an instrument) the subtle differences between the actual overtone and the harmonic frequencies will also contribute to the actual sound - or timbre - of an instrument.

You would need to expand on your question, I think, if you want more sense out of us.

Are you, perhaps, referring to 'beat frequencies' that are generated when two signals go through a system? These are not harmonically related to the input tones.

6. Dec 23, 2011

### oem7110

The frequency of sound is 1800 Hz, sound energy moves in sine wave with amplitude, does anyone have any suggestions on what kind of frequency I should use to reduce the amplitude of 1800 Hz sound energy?
Thanks in advance for any suggestions

7. Dec 23, 2011

### sophiecentaur

I'm sorry but I have no idea what you are asking. Could you try again?

8. Dec 23, 2011

### Bobbywhy

Since you want to reduce the amplitude of the 1800 Hz you could use the principle of destructive interference. Generate an identical sound wave of the same frequency and shift its phase by 180 degrees. When mixed the two will cancel completely.

9. Dec 23, 2011

### sophiecentaur

Cancellation using this method is vet unstable. Feedback can achieve cancellation inert a reasonably wide frequency range - as in noise cancelling headphones.

10. Dec 23, 2011

### oem7110

Based on the principle of destructive interference, the sound can be cancel completely on some specific spots, on another spot as sound is in phase, which would be louder and is not what I want, do you have any suggestions on reducing the amplitude of the 1800 Hz sound using different frequency based on destructive interference? so the sound will be destructed everywhere, rather than only on specific spots.
Thanks everyone very much for any suggestions

11. Dec 23, 2011

### sophiecentaur

How could a signal with a different frequency ever produce total cancellation? For cancellation to occur, the vectors need to be equal and opposite at all times. This can only happen if the two frequencies are identical and the relative phases are correct.

12. Dec 23, 2011

### oem7110

1800 Hz/2 = 900 Hz so 2nd harmonic of 900 Hz is 1800 Hz
1800/3 = 600 and 3rd harmonic of 600 is 1800
1800/4 = 450 - 4th harmonic is 1800
1800/5 = 360
1800/6 = 300
1800/7 = 266 2/3 (no one said they needed to be whole numbers!)
1800/8 = 225
1800/9 = 200
1800/10 = 180 -10th harmonic is 1800
and so on

Can 1800 Hz sound frequency be reducing its amplitude by using lower Hz of sound frequency? as shown above.

For ocurring destructive interference using same frequency, does cancellation occur only on specific spot by reducing the amplitude to 0? but on another spots, when sound wave in phase, will the 1800 Hz sound wave will be louder by doubling its amplitude?

13. Dec 23, 2011

### Bobbywhy

oem7110: It would be useful if you describe the situation you have and want to control in some detail. It would be helpful to those of us who try to give you suggestions to know exactly what problem you are trying to solve. Thank you.

Have you read posts #8, #9, and #11 above? As Mr. Sophiecentaur said, noise cancellation headphones completely cancel sounds by the vector addition of two sound waves...exactly out of phase (180 degrees) with one another.

What is the purpose of bringing up the subject of harmonics again? Why do you think harmonics might help reduce the intensity of your 1800 Hz sound?

Now, you ask: "For ocurring destructive interference using same frequency, does cancellation occur only on specific spot by reducing the amplitude to 0? but on another spots, when sound wave in phase, will the 1800 Hz sound wave will be louder by doubling its amplitude?"

Answer: cancellation occurs throughout the entire sound field providing the correct out-of-phase condition remains. What gives you the idea that it only happens in some areas?

14. Dec 23, 2011

### sophiecentaur

It is still not clear what you're after here. However, here are a few basics. You need an exact replica of a signal if you want to cancel another signal. You cannot produce an exact replica of a sine wave with a combination of sine waves of other frequencies - the Maths makes that quite clear.
Naturally, you can cancel a sine wave if you use any signal that happens to contain a component that is equal in amplitude and of opposite phase. A 'distorted' sub-harmonic will contain harmonics at your wanted frequency but I don't see that is relevant as you will also be introducing a load of other stuff which will be there after your wanted signal has been eliminated. Why not just start with a sinusoidal interfering signal of the right frequency in the first place?
And of course, as you say, the cancellation, even when possible, is only possible at locations where the relative phases are suitable - i.e at nodes in an interference pattern. Elsewhere, the sum of the waves wil have double amplitude. (Conservation of energy etc.)

There is another point (and this may be what you have been getting at) that you could generate harmonics of a low frequency signal in a non-linear circuit component like a diode that would cancel your 1800Hz signal if you were to get the phase right. In this case, the energy that you have eliminated will turn up in other parts of the spectrum and also be dissipated within resistive parts of the non-linear component.

15. Dec 23, 2011