On Jan 1, 8:35 pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On Tue, 01 Jan 2008 11:58:45 -0800, karthikbalaguru wrote:
> > Hi,
> > Why does a sinusoidal waveform alone does not have any harmonics or
> > distortion ?
>
> > For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
> > Sawtooth wave of constant period contains odd and even harmonics Square
> > wave of constant period contains odd harmonics Triangle wave, (an
> > integral of square wave) contains odd harmonics
>
> > But, How is it possible that sinusoidal wave alone does not have any
> > harmonics or distortion ?
> > I searched the internet,but i did not find any link/pdf that talks in
> > detail about these .
> > Any ideas ?
>
> > Thx in advans,
> > Karthik Balaguru
>
> Reading all the responses to this has been like hearing of all the wise,
> blind men who are describing an elephant.
>
> So, IMHO, an elephant is like a rope. And by the way, why is it suddenly
> raining fertilizer?
>
> At any rate, a sine wave doesn't have any because that's how harmonics
> are defined. Harmonics are defined in the context of the Fourier series,
> and the Fourier series for a pure sine wave is just -- that sine wave.
> That's it, no more. Only a periodic wave that deviates from a perfect
> sine wave can have harmonics, and (thanks to Fourier) we know that we can
> express that periodic wave, if we so choose, as a sum of sine waves at
> the fundamental frequency and all of it's multiples.

Thanks. I had similar thoughts to your's.

I had to giggle when Bartoli correctly said, as you did, that it
basically a definitional matter, and Allison jumped to the moon.

On Jan 2, 4:17 pm, "Richard Henry" <rphe...@home.com> wrote:
> <the.ioni...@gmail.com> wrote in message
>
> news:62cc912d-bdd9-44b2-825e-9050465d6e09@s12g2000prg.googlegroups.com...
>
>
>
> > On Jan 2, 8:58 am, karthikbalaguru <karthikbalagur...@gmail.com>
> > wrote:
> > > Hi,
> > > Why does a sinusoidal waveform alone does not have any harmonics or
> > > distortion ?
>
> > > For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
> > > Sawtooth wave of constant period contains odd and even harmonics
> > > Square wave of constant period contains odd harmonics
> > > Triangle wave, (an integral of square wave) contains odd harmonics
>
> > > But, How is it possible that sinusoidal wave alone does not have any
> > > harmonics or distortion ?
> > > I searched the internet,but i did not find any link/pdf that talks in
> > > detail about these .
> > > Any ideas ?
>
> > > Thx in advans,
> > > Karthik Balaguru
>
> > simple answer.. saw and square waves are made up of hundreds of sine
> > waves.. sine
> > wave is made up of one.
>
> Hundreds?

Yes, hundreds. The plural form of hundred, in other words AT LEAST 2
hundred.
An infinite number is consistent with "at least 2 hundred".



Mark

Simon S Aysdie wrote:
> On Jan 1, 8:35 pm, Tim Wescott <t...@seemywebsite.com> wrote:
>> On Tue, 01 Jan 2008 11:58:45 -0800, karthikbalaguru wrote:
>>> Hi,
>>> Why does a sinusoidal waveform alone does not have any harmonics or
>>> distortion ?
>>> For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
>>> Sawtooth wave of constant period contains odd and even harmonics Square
>>> wave of constant period contains odd harmonics Triangle wave, (an
>>> integral of square wave) contains odd harmonics
>>> But, How is it possible that sinusoidal wave alone does not have any
>>> harmonics or distortion ?
>>> I searched the internet,but i did not find any link/pdf that talks in
>>> detail about these .
>>> Any ideas ?
>>> Thx in advans,
>>> Karthik Balaguru
>> Reading all the responses to this has been like hearing of all the wise,
>> blind men who are describing an elephant.
>>
>> So, IMHO, an elephant is like a rope. And by the way, why is it suddenly
>> raining fertilizer?
>>
>> At any rate, a sine wave doesn't have any because that's how harmonics
>> are defined. Harmonics are defined in the context of the Fourier series,
>> and the Fourier series for a pure sine wave is just -- that sine wave.
>> That's it, no more. Only a periodic wave that deviates from a perfect
>> sine wave can have harmonics, and (thanks to Fourier) we know that we can
>> express that periodic wave, if we so choose, as a sum of sine waves at
>> the fundamental frequency and all of it's multiples.
>
> Thanks. I had similar thoughts to your's.
>
> I had to giggle when Bartoli correctly said, as you did, that it
> basically a definitional matter, and Allison jumped to the moon.
>
It isn't just a matter of definition. In classical mechanics, most
simple sorts of motion (a mass on an ideal spring, the motion of a point
on a rotating sphere, and so on) are sinusoidal. Sines and cosines are
the eigenfunctions of all sorts of vibrations, including drum heads.
(Drum heads go 'thump' instead of 'bonnnnggggg' because their sinusoidal
oscillations don't occur at evenly-spaced frequencies.)

Frequency-dependent loss, for instance due to damping, makes essentially
all vibrations become more and more like damped sinusoids as they die
away.

In optics, a (weak) sinusoidal grating produces only one diffracted
order (one on each side of the specular reflection). All other profiles
produce multiple orders.

In quantum mechanics, the time evolution of every eigenstate is
sinusoidal. Sinusoids are the only functions for which the Planck
relation e = h * nu applies.

So it isn't just a matter of definition--exponential functions,
including sines and cosines, really are fundamental to a wide range of
physical processes. Another way of saying this is that just about all
the equations of mathematical physics are second-order differential
equations.

Cheers,

Phil Hobbs

On Fri, 22 Feb 2008 14:08:32 -0800 (PST), redbelly
<redbelly98@yahoo.com> wrote:

>On Jan 2, 4:17 pm, "Richard Henry" <rphe...@home.com> wrote:
>> <the.ioni...@gmail.com> wrote in message
>>
>> news:62cc912d-bdd9-44b2-825e-9050465d6e09@s12g2000prg.googlegroups.com...
>>
>>
>>
>> > On Jan 2, 8:58 am, karthikbalaguru <karthikbalagur...@gmail.com>
>> > wrote:
>> > > Hi,
>> > > Why does a sinusoidal waveform alone does not have any harmonics or
>> > > distortion ?
>>
>> > > For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
>> > > Sawtooth wave of constant period contains odd and even harmonics
>> > > Square wave of constant period contains odd harmonics
>> > > Triangle wave, (an integral of square wave) contains odd harmonics
>>
>> > > But, How is it possible that sinusoidal wave alone does not have any
>> > > harmonics or distortion ?
>> > > I searched the internet,but i did not find any link/pdf that talks in
>> > > detail about these .
>> > > Any ideas ?
>>
>> > > Thx in advans,
>> > > Karthik Balaguru
>>
>> > simple answer.. saw and square waves are made up of hundreds of sine
>> > waves.. sine
>> > wave is made up of one.
>>
>> Hundreds?
>
>Yes, hundreds. The plural form of hundred, in other words AT LEAST 2
>hundred.
>An infinite number is consistent with "at least 2 hundred".
>
>:-)

---
Yes, but in the vernacular, 'hundreds' is considered to be, in the
limit, less than a thousand.

An apt comparison, using your method, might be to say that placing
rovers on Mars took tens of hours.

--
JF

On Feb 22, 6:32 pm, John Fields <jfie...@austininstruments.com> wrote:
> On Fri, 22 Feb 2008 14:08:32 -0800 (PST), redbelly
>
>
>
> <redbell...@yahoo.com> wrote:
> >On Jan 2, 4:17 pm, "Richard Henry" <rphe...@home.com> wrote:
> >> <the.ioni...@gmail.com> wrote in message
>
> >>news:62cc912d-bdd9-44b2-825e-9050465d6e09@s12g2000prg.googlegroups.com...
>
> >> > On Jan 2, 8:58 am, karthikbalaguru <karthikbalagur...@gmail.com>
> >> > wrote:
> >> > > Hi,
> >> > > Why does a sinusoidal waveform alone does not have any harmonics or
> >> > > distortion ?
>
> >> > > For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
> >> > > Sawtooth wave of constant period contains odd and even harmonics
> >> > > Square wave of constant period contains odd harmonics
> >> > > Triangle wave, (an integral of square wave) contains odd harmonics
>
> >> > > But, How is it possible that sinusoidal wave alone does not have any
> >> > > harmonics or distortion ?
> >> > > I searched the internet,but i did not find any link/pdf that talks in
> >> > > detail about these .
> >> > > Any ideas ?
>
> >> > > Thx in advans,
> >> > > Karthik Balaguru
>
> >> > simple answer.. saw and square waves are made up of hundreds of sine
> >> > waves.. sine
> >> > wave is made up of one.
>
> >> Hundreds?
>
> >Yes, hundreds. The plural form of hundred, in other words AT LEAST 2
> >hundred.
> >An infinite number is consistent with "at least 2 hundred".
>
> >:-)
>
> ---
> Yes, but in the vernacular, 'hundreds' is considered to be, in the
> limit, less than a thousand.
>
> An apt comparison, using your method, might be to say that placing
> rovers on Mars took tens of hours.
>
> --
> JF

You're absolutely correct. I was kidding around, sorry if that wasn't
obvious.

Mark

On Feb 22, 3:10=A0pm, Phil Hobbs <pcdhSpamMeSensel...@pergamos.net>
wrote:
> Simon S Aysdie wrote:
> > On Jan 1, 8:35 pm, Tim Wescott <t...@seemywebsite.com> wrote:
> >> On Tue, 01 Jan 2008 11:58:45 -0800, karthikbalaguru wrote:

> > I had to giggle when Bartoli correctly said, as you did, that it
> > basically a definitional matter, and Allison jumped to the moon.
>
> It isn't just a matter of definition...

It is a definitional matter.

Originally:
"Why does a sinusoidal waveform alone does not have any harmonics or
distortion?"

The fundamental ("alone") is the "first harmonic." That is, it is
self-referential which in ordinary language also comes out to
"definitional," "self-evident," "axiomatic" and other such lingo. It
is the _basis_.

You can look at it mathematically too. It is energy at a single
"line": cos(wt) for example. The single line "is what it is," and as
a _fundamental_ it refers to nothing else because that is what it
means to be fundamental. Anytime you end up having no choice but to
speak in tautology to "explain" something, it is a basis; it is
definitional.

Phil Hobbs wrote:

> Simon S Aysdie wrote:
>
>> On Jan 1, 8:35 pm, Tim Wescott <t...@seemywebsite.com> wrote:
>>
>>> On Tue, 01 Jan 2008 11:58:45 -0800, karthikbalaguru wrote:
>>>
>>>> Hi,
>>>> Why does a sinusoidal waveform alone does not have any harmonics or
>>>> distortion ?
>>>> For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
>>>> Sawtooth wave of constant period contains odd and even harmonics Square
>>>> wave of constant period contains odd harmonics Triangle wave, (an
>>>> integral of square wave) contains odd harmonics
>>>> But, How is it possible that sinusoidal wave alone does not have any
>>>> harmonics or distortion ?
>>>> I searched the internet,but i did not find any link/pdf that talks in
>>>> detail about these .
>>>> Any ideas ?
>>>> Thx in advans,
>>>> Karthik Balaguru
>>>
>>> Reading all the responses to this has been like hearing of all the wise,
>>> blind men who are describing an elephant.
>>>
>>> So, IMHO, an elephant is like a rope. And by the way, why is it
>>> suddenly
>>> raining fertilizer?
>>>
>>> At any rate, a sine wave doesn't have any because that's how harmonics
>>> are defined. Harmonics are defined in the context of the Fourier
>>> series,
>>> and the Fourier series for a pure sine wave is just -- that sine wave.
>>> That's it, no more. Only a periodic wave that deviates from a perfect
>>> sine wave can have harmonics, and (thanks to Fourier) we know that we
>>> can
>>> express that periodic wave, if we so choose, as a sum of sine waves at
>>> the fundamental frequency and all of it's multiples.
>>
>>
>> Thanks. I had similar thoughts to your's.
>>
>> I had to giggle when Bartoli correctly said, as you did, that it
>> basically a definitional matter, and Allison jumped to the moon.
>>
> It isn't just a matter of definition. In classical mechanics, most
> simple sorts of motion (a mass on an ideal spring, the motion of a point
> on a rotating sphere, and so on) are sinusoidal. Sines and cosines are
> the eigenfunctions of all sorts of vibrations, including drum heads.
> (Drum heads go 'thump' instead of 'bonnnnggggg' because their sinusoidal
> oscillations don't occur at evenly-spaced frequencies.)
>
> Frequency-dependent loss, for instance due to damping, makes essentially
> all vibrations become more and more like damped sinusoids as they die away.
>
> In optics, a (weak) sinusoidal grating produces only one diffracted
> order (one on each side of the specular reflection). All other profiles
> produce multiple orders.
>
> In quantum mechanics, the time evolution of every eigenstate is
> sinusoidal. Sinusoids are the only functions for which the Planck
> relation e = h * nu applies.
>
> So it isn't just a matter of definition--exponential functions,
> including sines and cosines, really are fundamental to a wide range of
> physical processes. Another way of saying this is that just about all
> the equations of mathematical physics are second-order differential
> equations.
>
> Cheers,
>
> Phil Hobbs
That is to say, X = -X'' (or -X double dot).

Robert Baer wrote:
> Phil Hobbs wrote:
>
<big snip>
>> So it isn't just a matter of definition--exponential functions,
>> including sines and cosines, really are fundamental to a wide range of
>> physical processes. Another way of saying this is that just about all
>> the equations of mathematical physics are second-order differential
>> equations.
>>
>> Cheers,
>>
>> Phil Hobbs
> That is to say, X = -X'' (or -X double dot).

That's an undamped oscillator equation, which qualifies but isn't the
only example...Maxwell's equations, the heat equation, the Schrodinger
equation, the harmonic oscillator equation with damping, the wave
equation--they're all second order linear DEs. (Laplace's equation is
too, but it doesn't have a time dependence.)

Cheers,

Phil Hobbs