Hi again,
For a single stage RC low pass filter the
-3db point is at w=1/RC. At any frequency above this point the
attenuation is going to be even more, so if you tune 1/RC even lower
by making R bigger you effectively increase the attenuation to the
signal to be rejected so you'll see less of it in the output. Unfortunately
this means the -3db point also gets closer to the pass frequency so
you'll get some more attenuation there too.
A double filter does twice the work and has a steeper slope too,
so it's sharper and this means it doesnt affect the pass frequency as
much for the same amount of rejection of the noice frequency.
In the book they may have assumed that this would be good enough,
or that the input noise was not equal in amplitude to the signal as
you have shown in your circuit. Usually the noise is lower than the
signal and if that is really the case then maybe one stage would work
ok. It also depends how clean the output signal really has to be...
noise 1/10 th of the pass frequency output is ok or do you need 1/100 th
of the pass frequency output. This specification affects the requirements
of the filter greatly.
Also, how much attenuation of the signal frequency is acceptable.
This affects component values as well.
A very strong filter can be built with three stages, where the resistance
of the first stage starts at 1k and the second stage has 10k and the last
stage has 100k, and the caps go 0.1uf, 0.01uf, and 0.001uf.
This has lots of cut at 16kHz and the output at 1kHz is around 0.6 of
the input (not too bad) and you'll get a very clean 1kHz signal.