Continuing on from the square wave example, the rise time is directly correlated to the frequency range the circuitry can handle.
If you know anything about Fourier analysis, the reason is clear. If not, here's a quick explanation for the special case of a square wave:
Mathematically, a square wave (of frequency
f) can be made up by adding an infinite number of sine waves, using a formula that goes something like this:
1/
1 sin(1*f) +
1/
3 sin(3*f) +
1/
5 sin(5*f) +
1/
7 sin(7*f) + ...etc. Yes, they are all the odd harmonics - at reduced amplitudes, the higher the frequency you go.
In this formula, the factors 1, 3, 5, 7, etc... can go on forever, but the following diagram shows how how the mathematical shape gets closer to a real square wave using more terms. In this, the number 'K' is the highest numbered factor used.
So, for K=1, the formula is simply
1/
1 sin(1*f).
For K=5 the formula is
1/
1 sin(1*f) +
1/
3 sin(3*f) +
1/
5 sin(5*f)
For K=11 the formula is
1/
1 sin(1*f) +
1/
3 sin(3*f) +
1/
5 sin(5*f) +
1/
7 sin(7*f) +
1/
9 sin(9*f) +
1/
11 sin(11*f)
... and so on.
As you can see, the higher the frequencies that are pumped into this formula, the closer the resultant waveform is to an 'ideal' square wave. You will notice the rise time of the square wave is faster as the included frequencies range higher.
This is why - if you have a 100Mhz square wave and you want to display it on an oscilloscope, you will probably want a scope capable of 1GHz ... or maybe more.