Do square, sawtooth, and triangular waves exist in nature?

[PainterGuy]

Hi,

Wate ripples closely resemble sinusoidal waves which means sine waves exist in nature. Do square, sawtooth and triangular waves exist in nature, or, have they been invented for their special characteristics? Help me, please. Thanks

Cheers,

 

[Delta Kilo]

Clarinet produces roughly square wave.

 

[bp_psy]

Technically there are no sine waves in nature. The sinusoidal functions are just pure mathematical concepts that can be used to approximately describe some physical phenomena.The square ,triangle ,sawtooth function are also mathematical concepts that can approximately describe some phenomena.You can generate signals that are approximately square, triangles,sawtooth with pretty simple circuits.

 

[Delta Kilo]

Well, sine wave is special, being a solution of x''=-kx. It is produced by a simple harmonic oscilaltor, which can be basically anything that obeys F=-kx law. A lot of non-linear real-world systems are approximated quite well by linear F=-kx law for sufficiently small values of x. So as long as there is a force oppposing the displacement and the dissipation is sufficiently small, the system will be capable of oscillating and the smaller the displacement the closer it is going to be to sine wave.

To produce square, triangular or sawtooth wave you would need rather special non-linear process. This can happen but it would be rare. A geyser would be an example of such system, I guess the pressure inside would look like a sawtooth.

 

[russ_watters]

To produce square, triangular or sawtooth wave you would need rather special non-linear process. This can happen but it would be rare. A geyser would be an example of such system, I guess the pressure inside would look like a sawtooth.

Square wave: day and night vs time.

 

[LostConjugate]

Square wave: day and night vs time.

That isn't square?? Its more of a Sin wave.

A Square wave is just a superposition of a whole lot of high frequency sin waves and a few lower frequency ones for the basic shape. There is not much before humans came along that could produce so many high frequency waves, but humans invented mechanical units that produce square waves and so now they exist in nature, since we are part of nature. Same goes for any other sort of wave, ones that require very specific high frequency interference to produce hard edges usually being the product of intelligent design.

Recommended:
http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-11/

 

[olivermsun]

Wate ripples closely resemble sinusoidal waves which means sine waves exist in nature.

While it is commonly taught that water waves resemble sine waves, one rarely if ever actually observes water waves which really look sinusoidal.

 

[schip666!]

For sound, a bowed instrument approximates a sawtooth due to the bow grabbing and then releasing the string. Plucked or struck instruments may have a square-ish envelope. Because of the resonant tube I'm not sure reeds, like the clarinet, output a square, but the driving force of the reed is close. I can't offhand think of a triangle example, but it is a slightly "distorted" sine so...phase aside...most musical sounds we hear might approximate one.

 

[russ_watters]

That isn't square?? Its more of a Sin wave.

Youre talking about altitude. Day/night are binary conditions. Any repeating binary condition will plot as a square wave.

 

[xts]

sawtooth:
length of grass vs time on my lawn.
I mow it once a week.

 

[bp_psy]

sawtooth:
length of grass vs time on my lawn.
I mow it once a week.

Are you sure that grass length vs time is linear?

 

[nitsuj]

Technically there are no sine waves in nature. The sinusoidal functions are just pure mathematical concepts that can be used to approximately describe some physical phenomena.The square ,triangle ,sawtooth function are also mathematical concepts that can approximately describe some phenomena.You can generate signals that are approximately square, triangles,sawtooth with pretty simple circuits.

Mathematical concepts derived from observing nature, right?

If that can be swallowed, then from a mathematical perspective these waves exist in nature.

 

[LostConjugate]

Youre talking about altitude. Day/night are binary conditions. Any repeating binary condition will plot as a square wave.

I didn't think there was a specific time that it becomes night or morning though. I guess if we define a time then it would be a square wave. It is not related to the natural process of day night though.

 

[nitsuj]

Are you sure that grass length vs time is linear?

All else equal I can't see how it couldn't be.

 

[xts]

Are you sure that grass length vs time is linear?

As a first approximation? Seems to be OK...
Next week I'll try to make a series of measurements, 3 times a day shoud be feasible.

 

[nitsuj]

I didn't think there was a specific time that it becomes night or morning though. I guess if we define a time then it would be a square wave. It is not related to the natural process of day night though.

I'd have to disagree. Sunset/rise I would guess is defined as when the sun breaks the horizon. Seems binary to me, and absolutely the way natural process of day night.

It was a good example.

 

[bp_psy]

Mathematical concepts derived from observing nature, right?

This is a philosophy of mathematics question and there are many ways to look at it.
http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Contemporary_schools_of_thought

If that can be swallowed, then from a mathematical perspective these waves exist in nature.

I personally do not like to say things "the mathematical object x exists in nature" because:
1. All mathematical objects have characteristics that are different that the thing that inspired them.
2. Sometimes a physical phenomena can be modeled using different mathematical models.

 

[Jeff.N]

The displacement of a point of string on a string instrument arbitrarily near the bridge or bow over time is approximately somewhere between a saw and a triangle wave. Each period is composed of 2 straight lines, one increasing one decreasing, and the function is continuous.

Saw and Square waves are special cases of waves which each period is composed of 2 straight lines. (Saw is the case where 1 is vertical, triangle is the case where both lines have equal length and the total function is continuous.)

The graph of velocity of said point thus resembles a square wave.

http://www.abdn.ac.uk/~mth192/html/music.pdf pg 95

 

[russ_watters]

I didn't think there was a specific time that it becomes night or morning though. I guess if we define a time then it would be a square wave. It is not related to the natural process of day night though.

There is: they are defined in terms of sunrise and sunset. Ie, the summer solstice is the longest day of the year.

Not sure why you would say it is unrelated to a natural process, though.

 

[nitsuj]

This is a philosophy of mathematics question and there are many ways to look at it.
http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Contemporary_schools_of_thoughtI personally do not like to say things "the mathematical object x exists in nature" because:
1. All mathematical objects have characteristics that are different that the thing that inspired them.
2. Sometimes a physical phenomena can be modeled using different mathematical models.

"the mathematical object x exists in nature"
Taken literally, no one would agree with that.

Given how we have defined nature with this context, Mathematics is nature quantified.

A wave function is a mathematical expression of nature.

The nature of these statements is not philosophical (pun intended).

 

[ModusPwnd]

I would emphatically say that no, they do not exist in nature (presuming that existing as a concept in a human mind is somehow not sufficient to being nature)

 

[ajthrax1]

While it is commonly taught that water waves resemble sine waves, one rarely if ever actually observes water waves which really look sinusoidal.

...Dude are you serious?? Try dropping a stone (or almost any object) in a pool.

 

[Pythagorean]

For a real-time signal to from 0 to X in 0 time would take infinite energyclassically, so square/rectangular and sawtooth waves are out. I think the discontinuity between peaks and troughs of triangular causes similar problems, but not sure.

There is: they are defined in terms of sunrise and sunset. Ie, the summer solstice is the longest day of the year.

Not sure why you would say it is unrelated to a natural process, though.

The point is that it's a high level of abstraction. No matter how you define a day and a night, there is no meaningful transition in the classical physical universe that takes place in 0 seconds. You have to draw a line arbitrarily and make your function drop to 0 between samples when that arbitrary line approaches. And even though that arbitrary line is governed in some approximate Euclidian time-frame via atomic clocks, there will, always be slips, lags, and hiccups in the cycle because the abstraction of "day" and "night is the result of a very complicated N-body problem involving the nearest giant bodies.

 

[Pythagorean]

...Dude are you serious?? Try dropping a stone (or almost any object) in a pool.

he's serious; you're imagining sin waves in the water ripples. Have you seen real water ripple profiles? Firstly, they're three dimensional objects, a sinwave is one dimensional. But more importantly, even if you look at a slice like you'd like to, there are particular asymmetries when comparing front of the wave and the back of the wave, since each is facing a different inertial tensor in a real dynamical moment of water ripples. There also turbulent effects.

You would be right to say it is a good approximation for second-order accuracy, but regardless, there's nothing wrong with oliver's statement.

 

[sophiecentaur]

Are you sure that grass length vs time is linear?

It could well be exponential because the growth rate will be proportional to the number of cells that make up its length. But the rate of food supply could affect the growth rate and there may be regulating mechanisms which could govern the growth rate more powerfully than my simple exponential model, which assumes a constant rate of cell division.

I plotted the growth of a Christmas Cactus cutting in my office, many years ago. It was pretty damn close to exponential over several months. How nerdy!

 

[olivermsun]

...one rarely if ever actually observes water waves which really look sinusoidal.

...Dude are you serious?? Try dropping a stone (or almost any object) in a pool.

Dude I am serious. The circular spreading makes them not plane waves.

 

[olivermsun]

For a real-time signal to from 0 to X in 0 time would take infinite energyclassically, so square/rectangular and sawtooth waves are out. I think the discontinuity between peaks and troughs of triangular causes similar problems, but not sure.

You do actually see sawtooth-like waves with very vertical slopes -- look at waves in the surf zone right before they break!

 

[sophiecentaur]

All these waves are definitely not sinusoidal - but neither are they triangular or square. There are very few such waves in nature because, in the end, they all have rounded or 'ringing' edges. It all depends on how approximate you are prepared to be in describing them as sawtooth.
Even the water surface wave only looks sinusoidal for very small displacements. They very soon start to look 'peaky' because there is both longitudinal and transverse displacement.

 

[Pythagorean]

You do actually see sawtooth-like waves with very vertical slopes -- look at waves in the surf zone right before they break!

Yes, we see sine-like waves and square-like waves too.

But we could, for instance, closer approximate the sigmoidal transitions of a square-wave with a hyperbolic cosine.

 

[hisham.i]

I was thinking about the relation of the growth of our bones with respect to time, i think it looks like a simplified hyperbolic tangent (simplified sigmoid).