Maths Help!!

[Mattt]

Mathematical question for you!

I need to work out the length of a Sine wave – related to piping, and joints of unequal diameter tubes.

The line has a maximum value ‘R’ (100) and minimum value ‘d’ (96.825).

It completes 2 full cycles between 0 and ‘Y x Pi’ (314.159) – which gives a frequency of ‘0.5 x Y x Pi’ (157.08).

I was hoping there is a Maths/Engineering guru who would be able to let me know the answer to this example (in brackets) and the general formula I need to calculate for other examples.

Virtual pint to the winner!!

[esuuv]

right - i've read it about a hundred times and it still makes no sense, please can you give some context? shock waves in fluids I presume?

Edited by esuuv on Thursday 15th October 10:48

[ewenm]

"length of a sine wave"? Do you mean the actual length of the curve or the wavelength (distance between two peaks) or something else?

[WorAl]

I thought Pi was 3.141592?

[Superhoop1904]

Its too early.......

[Mattt]

Sorry, it has been a long time since I did this, I re-reviewed my numbers:

The formula of the Sine wave is 'y = 6.699 x cos(theta)'

This gives me the wave I need, between 0 and Pi.

I need 2 cycles of this wave, so from 0 to 2 x Pi.

The same curve is replicated in reality where 2 x Pi = Circumference of a pipe (in this example 314.159mm).

I need to know the length of the 2 cycles of the wave - so I know the length of the end of the pipe, because if you picked up the graph and wrapped it round, it would be identical to the end of the pipe.

Is that clearer, or do need to explain better still?

[Mattt]

ewenm said:

"length of a sine wave"? Do you mean the actual length of the curve or the wavelength (distance between two peaks) or something else?

Actual length of the curve, not the wavelength.

[spitfire-ian]

Mattt said:

The same curve is replicated in reality where 2 x Pi = Circumference of a pipe (in this example 314.159mm).

I'm sure that 2 x Pi will always equal 6.28.

Are you on about the formula for working out a circumference which is 2 x Pi x R?

[Mattt]

I was just saying Pi for the wave as that's what they give in examples as the end point.

In terms of degrees, the graph would go from 0 to 720 - where 720 degrees would represent the circumference of a pipe (in this example 314.159mm).

[Planet Claire]

Does this help?

http://mathforum.org/library/drmath/view/52038.htm...

[Mattt]

I've just solved it using trapezoidal sampling, not exact, but better than nothing!!

[Gareth350]

Is the answer, "the great wall of china?"

[the-gofer]

Mattt said:

I've just solved it using trapezoidal sampling, not exact, but better than nothing!!

You are after the arc length of a sine curve. You need an elliptical integration (not dissimilar to trapezoidal sampling I guess) of the function y=sin(x) for x of 0->2pi. Wikipedia shows the derivation of the integral if you are interested, but the short answer is apparently 7.640395578 (I haven't calculated this btw, the value appears consistently in various answers that I "googled").

If your curve is actually y=a.sin(x) where a is the amplitude then the answer would presumably be 7.64a.

Doesn't sound much when 0<x<6.28 but I guess if you imagine flattening the line out it feels about right: