The 0.35 formula thing is for rise time. Don't worry about that yet, you need to understand basic bandwidth and the -3dB point as a first step.
Dave.
Rise time and frequency is highly related each others.
Maybe you SuperMiguel, have read oscilloscope xyz?
(there is good explanation about ythese things example in Agilent and Tektronix "library".)
As we know square pulse (or what ever shape signal) can think as series of sine waves.
Good thumb rule is... if you look 30MHz square wave pulses so that you can also see it as practice square wave... you need at minimum 9th harmonic without markable attenuation. So it need minimum 270MHz (~300MHz) scope if bandwidh is gaussian type. (becouse over 300MHz it can still show something and it gives littlebit more rise time on the scope screen. If it is brickwall bandwith same risetime need maybe 400MHz brickwall BW scope.)
This in normal case. It specially is dependent about real risetime what signal have and what we then also want see and inspect.
Risetime is just most important (and risetime also tell some aproximation about scope BW)
If you have example 10MHz square wave but risetime is 2ns... for analyze this 2ns rising or falling edge or corners it need in practice much more fast oscilloscope so that you measure signal and not oscilloscope and probes itself. In thumb rule (in my own "standards") it need 0,2 - 0,5ns risetime scope. If look one shot real time it need be 100 or 200ps sampling period... so it need 5 - 10Gs/s realtime. Then you can tell that you really can analyze reliable what happends there in rising edge. This kind of scope is not modified rigol or mid-level agilent. And we have only 10MHz square wave... so. Do not mix Hz and risetime if you are looking fast rise- or falltime pulses and want analyze these.
0.35 rule and MHz BW can use for thinking risetime and maximum sinewave frequency. (and remember square wave is series of odd harmonics)
If you take 10MHz scope and look 10MHz square wave you can see some kind of littlebit distorted sine (becouse BW is not exactly stopping 10MHz)
There is no any fixed rule (only common practice) for -3dB. It is only some manufacturer who tell that BW is example 100MHz. They tell signal (sinewave) attenuation compared to reference frequency with same amplitude input signal. But many times also this is only half true.
I have seen example that they tell 2 points... example some use 50kHz reference level so that input signal level is example 6 div (vertical) on scope screen. (not full 8 or 10 div)
This is set as reference point. After then they look what is first higher frequency where signal drops 3dB in scope display (or measured V level).
But who tell that in frequency response have any highs or lows between these points or from zero freq to reference point! I know this problem becouse I have repair/service and calibrated hundreds of different scopes /analog and digital, old and new ones. mainly HP and Tektronix.
What is important for selection oscilloscope... (in this BW - risetime quesion). You need know most fast risetime what you need inspect. (also this is not whope truth) Some times need go more deep... equipment designed risetime... but we are inspecting all possible troubles... then need think more deep... if need also know something more deep about pulse edges... example sometimes signal road quality... if matching is mad... there may find some high freq components... (short time components becouse pulse transfer line is bad)
In thumb... if look digital pulse signals... use minimum 10 x pulse frequency. (but higher frequencies it is not exactly true need always)
IF you look only sinewaves... example radio transmitter or radio receiver IF or something like it... or audio signals... then you need only 1-3x your main frequency (becouse many timesw still want littlebit know about signal shape if there is something (example high harmonic 2. 3. levels.)
There are also this kind of things: sometimes good 3mpix camera make lot of better picture than poor 12 or higher Mpix camera. Analog channel quality is just nearly as lense in camera. (outside scope is probe and inside scope is whole all before AD conversion, this whole analog route quality to ADC is many times more important than we think if we only look megasamplerates and MHz on the scope front panel.