Graphic of function similar to Sin(x) but with scaled size

Question

I wont to build a graphical representation of numbers, as "waves":

Similar as the graphic of sin x but for each number N it gets bigger and bigger crosses the x axes in the multiples of N,
with y from -N to +N
and repeating every 2N.

I found this tool usefull for the drawing:

http://www.wolframalpha.com/

Can some one help me with finding the function ?

Answer 1

I am not entirely sure what you mean, but I can give you a direction to look.

To change the points where the graph crosses the x-axis, change sin(x) to sin(a*x) for some a. For example sin(pi*x) or the other way round using a division: sin(x/pi).

To make the graphic bigger for bigger x, try adding a factor related to x (like x itself, x^2, sqrt(x), e^x). For example: x*sin(x)

Answer 2

Found it:

f(x) = n*(sin (pi*x/n))

http://www.wolframalpha.com