Linear amp emitter capacitors choice for 20Hz audio app

This is self assigned homework, so don't bother if this circuit is impract ical. I'm just following the basics.

With reference to a common emitter degenerated linear amplifier with partia l bypassed emitter resistor (figure 2.39 of Arts of Electronics 2nd Ed.), I 'm trying to figure out the value in Farads for the emitter bypass capacito r, for an audio amplifier (smallest frequency of interest of 20Hz).

In my design the un-bypassed emitter resistance is

r_E =20 Ohm

Quiescent current I_CQ is 2.5mA, so the BE junction inner resistance r_e is roughly V_T/I_C =25/2.5=10 Ohm

The book states that "the bypass capacitor is chosen by making its impedanc e small compared with r_e", but in that case did not deal with the addition al un-bypassed resistance r_E.

By introducing r_E, I guess the previous sentence should be rephrased with "the bypass capacitor is chosen by making its impedance small compared wit h r_e+r_E =10+20=30 Ohm".

Now, the book deals with a lowest admitted frequency of 650Hz, but in my ca se f_c is 20Hz.

So I need a capacitor whose impedance @20Hz is smaller (lets say .. ten tim es smaller?) than 30 Ohm:

Z_C (f_c) =1/(2 pi f_c C)