### Author Topic: Do all kind of vibrations follow simple harmonic motion rule? Please edify.  (Read 6029 times)

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#### Cerebus

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #25 on: November 09, 2016, 01:08:05 pm »
There's no doubt that the physical pressure wave has a sawtooth form. You can model this as a weighted sum of a lot of sine waves but those are imaginary, you can't physically measure any sine waves without filtering (i.e. applying a mathematical transformation).

I wouldn't be so sure. You can also extract frequencies through physical effects. Somebody humming can cause a tuning fork to vibrate, if they are tuned to the same frequency. Diffraction and refraction also can be used to filter physical waves - it isn't a purely 'mathematical' transformation.

By introducing a mechanical filter or resonance you've altered the underlying physical system. The sine wave wasn't there before you did that. I did deliberately pick the physically generated sawtooth as something that doesn't, per se, have a physical fundamental sine wave like a plucked string.
Anybody got a syringe I can use to squeeze the magic smoke back into this?

#### Tomorokoshi

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #26 on: November 09, 2016, 01:14:10 pm »
On a related topic, this series on the Michaelson Harmonic Analyzer is very interesting:

#### sainbablo

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #27 on: November 09, 2016, 10:34:42 pm »

You've got to love somebody who wishes to be edified.
[/quote]

"More than the calf wishes to suckle, the cow yearns to be suckled" A quote recalled, reading from a book of Physiology, decades ago
in good old UK ( it still is)

#### sainbablo

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #28 on: November 12, 2016, 03:39:36 am »
After going through posts of all the participants  if I put forth a conclusion that
physical sciences like Maths, possess quality that is, its terrestrial results are predictable and as well are
applicable to study of various objects in outer space but in case of human beings its scope is limited
owing to the fact that human's structure being biological, limit Maths scope of applicability, am I right
coming to that  conclusion?

« Last Edit: November 12, 2016, 03:42:59 am by sainbablo »

#### TimFox

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #29 on: November 12, 2016, 04:49:40 am »
In a non-EM context, consider the overtone content of actual musical instruments.  Overtones are the higher-frequency tones in a musical note, and are not necessarily harmonics.
For one-dimensional instruments, such as vibrating strings and narrow organ pipes, the overtones will be very close to harmonics (integer multiples of a fundamental).
For two-dimensional instruments, such as the kettle drum, the overtones are not harmonic.
See http://circularscience.com/about-drums for a discussion of overtones from a circular diaphragm.

#### sainbablo

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #30 on: November 12, 2016, 06:17:14 am »
In a non-EM context, consider the overtone content of actual musical instruments.  Overtones are the higher-frequency tones in a musical note, and are not necessarily harmonics.
For one-dimensional instruments, such as vibrating strings and narrow organ pipes, the overtones will be very close to harmonics (integer multiples of a fundamental).
For two-dimensional instruments, such as the kettle drum, the overtones are not harmonic.
See http://circularscience.com/about-drums for a discussion of overtones from a circular diaphragm.

Quite so. My understanding is that the vibrations emanating from one or two dimension sources when  striking the ear membrane  assume
a characteristic head setting ear membrane in to and fro motion ie towards interior( to wards middle ear) and outwards (towards the ear passage), which again is a replica of simple harmonic motion,and the membrane converts wave form to mechanical energy for transmission to internal ear.

To generalize I would say that range of audible frequencies from 64 to just about  4096 c/s (general terms)  is so  perceived
Now each of these instruments have 'character' of its own so that even with eyes closed one would name the source.
So  violin, or drums, or harmonica, being some examples of  string,percussion and reed instruments reveal their nature to the listener.

My question is what is the basis of individuality of each of these  instrument as is distinguished by the hearer?
Conceeded that the output of strings have no recource to internal reflection as  have pipe instruments producing over tones, yet
ear separates them.
My idea is that the head of the wave form and its shape striking the ear membrane has role in it.
What then, is the physical nature of that wave form?

Here I may have some what deviated from main topic but even at the risk of cross purpose, perceiving your musical proclivity, I
feel encouraged to invite your attention.

#### Loboscope

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##### Re: Do all kind of vibrations follow simple harmonic motion rule? Please edify.
« Reply #31 on: November 12, 2016, 09:29:35 am »
Hearing sounds is a task done by our ears, identifying sounds is a task done by our brain. Normally no one can identify musical instruments if he has not learned before, how these instruments will sound.
But if you regard the hearing processes in our brain, you will become aware, that our brain is a champion in identifying sounds nevertheless how complex they are and how complex might be the hearing situation (for example when you talk to persons in a noisy environment). You can find lots of details about this item in this book: "Auditory Neuroscience - Sense of Sound", Jan Schnupp et al, MIT Press 2012.

Musical instruments can be identified by two characteristics: one is the harmonic structure of the overtones, especially the individual patterns created by the different instruments/voices, the so called formant frequency (by the way: the cymbals are the musical instruments with the most inharmonic overtone structure, much more noise than sound, but the different cymbals will sound very different and characteristic and can easily be distinguished by a musical skilled ear).
The other is the very complex and very individual pattern of the first moment when the tone starts resp. the tone is created by the player: the transient phenomenon (german: "Einschwingvorgang"). In this part of one second a relatively chaotic pattern of frequency, noise etc. may appear, but these patterns are very individual for any instrument etc. and will be an essential held for identifying the sound of the different instruments. For example: if you will cut this first initial moment of the tone and let only hear the steady sound afterwards, also skilled ears often will not more distinguish the sound of clarinet/oboe/ soprano-sax.

Smf