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

1. Aug 16, 2011

### 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,

2. Aug 16, 2011

### Delta Kilo

Clarinet produces roughly square wave.

3. Aug 16, 2011

### 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.

4. Aug 16, 2011

### 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.

5. Aug 16, 2011

### Staff: Mentor

Square wave: day and night vs time.

6. Aug 16, 2011

### LostConjugate

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/...nd-waves-fall-2004/video-lectures/lecture-11/

7. Aug 16, 2011

### olivermsun

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

8. Aug 16, 2011

### 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.

9. Aug 16, 2011

### Staff: Mentor

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

10. Aug 16, 2011

### xts

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

11. Aug 16, 2011

### bp_psy

Are you sure that grass length vs time is linear?

12. Aug 16, 2011

### nitsuj

Mathematical concepts derived from observing nature, right?

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

13. Aug 16, 2011

### LostConjugate

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.

14. Aug 16, 2011

### nitsuj

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

15. Aug 16, 2011

### xts

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.

16. Aug 16, 2011

### nitsuj

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.

17. Aug 16, 2011

### bp_psy

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
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.

18. Aug 16, 2011

### 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

Last edited by a moderator: Apr 26, 2017
19. Aug 16, 2011

### Staff: Mentor

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.

20. Aug 16, 2011

### nitsuj

"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).

Last edited: Aug 16, 2011