Wikipedia:Reference desk/Archives/Mathematics/2007 March 18

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March 18

Generic plot diagrams

I'm wanting to produce some clear, simple time-domain and frequency domain plots of audio signals for a audio processing assignment I'm working on. Audacity does both, but I want to produce more "generic" plots where the particular GUI of the audio editor is not visible. For instance, if I want to display the time-axis information in Audacity, I have to show other parts of the program which is most undesirable.

http://img.waffleimages.com/2125764ae49011cfd7de2c41f1d106b708c6cb7e/img24.png

The picture above is an example of what I'm looking for. In particular, there are horizontal and vertical lines at the marked values for the axes. Naturally, I'll want control over how "zoomed in" I am to a specific plot, vertically and horizontally, and make it simple to load in any wave file.

My assumption is that more customisable, generic plots can be produced using some kind of maths package , but if there's a nice GUI program for outputting custom generic plots that would be preferred. Thanks. 164.11.204.51 18:34, 18 March 2007 (UTC)

If you're looking for free software, you could check out the tools listed in Category:Free plotting software. If you are using Linux, you may be specifically be interested in Category:Linux graph plotting software (all of which is listed as free). See also Wikipedia:How to create graphs for Wikipedia articles.  --Lambiam^Talk 20:40, 18 March 2007 (UTC)

In particular, I need to plot information from audio files (wave e.t.c) in domains and ranges of my choice. The wikipedia tutorials don't seem to point towards anything like this, although I'm sure there must be a function in a free windows plotting software to do this? —The preceding unsigned comment was added by 164.11.204.51 (talk) 22:31, 18 March 2007 (UTC).

You probably want the computing reference desk for this. Think of this as a two stage process 1) extract sutible numeric data from a wav, 2) plot it. I'd guess your more likely to find two different bits of software for the different tasks, and the CS desk may be able to help with 1). It might also be worth looking at some of the visulisation effects for winamp and similar, many of these are based around processing the audio data and turning them into visuals. Maybe theres some code you can hack out of one of these. --Salix alba (talk) 23:07, 18 March 2007 (UTC)

Differentiation of Trig

Why is the derivative of sin(x) only cos(x) when x is measured in radians? Algebra man 18:56, 18 March 2007 (UTC)

To avoid all ambiguity, let sinrad denote the sine function whose argument is in radians, and likewise for cosrad, so ^d/_dxsinrad(x) = cosrad(x). Define

sinscaled_a(x) = sinrad(2πx/a),

and again likewise for cosscaled. So, for example, sinscaled₃₆₀(x) gives the sine of angle x measured in degrees. Now, by the chain rule,

^d/_dx sinscaled_a(x) = ^d/_dx sinrad(2πx/a) = cosrad(2πx/a) ^d/_dx(2πx/a) = (2π/a) cosrad(2πx/a) = (2π/a) cosscaled_a(x),

This only equals cosscaled_a(x) if a = 2π. I hope this qualifies as a "reason".  --Lambiam^Talk 19:25, 18 March 2007 (UTC)

The working out of the derivative of sin(x) requires the sine of small angles rule which states that sin(x)~x only when x is in radians. Alexs letterbox 06:41, 19 March 2007 (UTC)

Which is quick to show informally. Define a radian as 1/(2π) of a circle. Start from a point x = r on the positive x axis, and draw a very short arc, moving through θ radians counter-clockwise. Then draw a line from the top of that arc to the origin. This gives an almost-triangle, except that the short side is an arc, not a line. For a short arc that's negligible, though, so we can pretend that the arc is a line, and that our shape is a triangle. (It's actually a sector of a circle, like a slice of cake.)

The long sides are both the same length r, because the shape is a sector of a circle. The arc has a length of θr. (If it were the entire circle, then θ would be 2π, so we would have the familiar formula for the circumference of a circle, 2πr.) The angle θ was very small, and the angles of a triangle should sum to 180 degrees; this means that the other two angles are almost ninety each, so we have a right triangle. The sine of θ is equal to opposite/hypoteneuse = θr/r = θ. If we were using different angle units, and not radians, then the formula for the arc length would have been different.

The first answer sort of begs the question, I think. I hope this is more convincing. —The preceding unsigned comment was added by 71.192.58.216 (talk) 10:03, 19 March 2007 (UTC).

All the information is in the preceeding answers; I shall attempt a synthesis.

• The derivative of a function f at a point x is the ratio of a small displacement in input from x divided into the resulting small displacement in output from f(x).
• Therefore sin(2x) will have a derivative twice as large as sin(x), for example; and in general the derivative will depend on the units of input. (This is true for any non-constant function.)
• At x = 0, cos(x) is exactly 1 no matter what input units we use.
• Therefore we can have only one possible choice of input unit for the sine function if its derivative is to match.
• Radian measure (arc length) works, as shown by a geometric argument.
• Therefore radian measure is the unique measure permitting the derivative of sin(x) to be cos(x').

This line of reasoning does not prove that the correspondence holds for all values of x, but it does show that if it is to hold at all, we must use radians. (I assume that anyone who could handle the general proof wouldn't be asking this question.) --KSmrq^T 23:36, 19 March 2007 (UTC)

Trend and Pattern

I am analysing some biological data, and am having to comment on the trend and pattern in the data. I was wondering if any statisticians could tell me what exactly is the difference between a trend and pattern in data ??? 89.241.4.129 19:40, 18 March 2007 (UTC)

If you plot some data as dependent on other data, and the plotted points seem equally scattered around a steadily increasing or decreasing curve, this reveals what is usually called a "trend". Often but not necessarily the independent variable is time. The concept of "pattern" is much more general; it can be applied to any recognizable regularity, for example that some variable usually registers lower during weekends than on workdays. See also Trend estimation.  --Lambiam^Talk 20:55, 18 March 2007 (UTC)

Please help really hard

please help me with these questions there reallyy hard the answers can only be between 1-31

1. A number n where if the sum of the digits of the number is divisible by n, then the number itself is divisible by n.
2. A number that is neither prime nor the sum of two distinct primes.
3. The only perfect number of the form x n + y n
4. The largest integer that is not the sum of two or more different primes.
5. The maximum number of pieces into which a pizza can be cut by making 6 cuts

if you could just answer these for me id be so greatful you have no idea thanks to anyone who can answer them for me remember the answer can only be between 1-31.

thank you, anon —The preceding unsigned comment was added by 68.193.39.27 (talk) 22:53, 18 March 2007 (UTC).

Unfortunatly (for you anyway) we cannot do your homework for you. And these are (for me) difficult questions to give clues for without giving you the answer. - Akamad 04:38, 19 March 2007 (UTC)

These questions are weird (and some of them are ridiculously easy). I'll get you started. For number 1, take any one-digit number. For question 2, how about the number 4? See what I mean? Just think about them for a second. –King Bee ^{(τ • γ)} 20:02, 19 March 2007 (UTC)

you guys suck. i better have not failed my project because of you.