Active Filters in Multiple Order

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Hi Guys.

I have a question on the behavior of active filters (low/high/band) that are connected serially in multiple order magnitude.

For instance given 2 low pass filters.

Now I understand there exists a -6dB/octave cutoff, and generally f_o or the -3dB value is situated at the x-intercept of a graph showing frequency vs gain.

If there are multiple filters, such as 2, then I understand this changes to a -12dB/octave, and so forth as more filters are attached with the same resistor/capacitor values etc.

Now my question is let's say someone asks to find f_4, or f_10, generally how does one go about calculating this? If there was just one LPF with f_0 of 1000Hz, than f_2 is -6dB/octave so it would be half as much, am I correct? How does this apply to a 2 LPF design, would it be 1/4 as much?

 

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so I think I should clarify

that f_2 would be (A = 2, or gain equal to 2?)

so in a bode plot with log f vs log A, the more integrators/low pass filters added would make the line much more steeper am I correct?

Thus for a single LPF (low pass filter), if F_o = 1000 Hz, then F_2 = 500 Hz at (Av = 2).

For a dual LPF configuration of same R/C values, if F_o = 1000Hz, then F_2 would be equal to 250 Hz, 4 times smaller since its -12db/octave??

is this logic correct?