An astable multivibrator has no stable state; it continuously oscillates between HIGH and LOW, generating a square wave without any external trigger. Its timing is set by charging and discharging a timing capacitor (C) through resistors, so the switching period is directly governed by the RC time constant.

For the common 555-timer astable configuration, the output frequency is:

f = 1.44 / ((R_A + 2R_B) × C)

The key point is that frequency is inversely proportional to the capacitance. A larger capacitor takes longer to charge to the upper threshold and discharge to the lower threshold, so each cycle takes more time (lower frequency).

Doubling only the capacitor (C → 2C), while keeping R_A and R_B the same:

f_new = 1.44 / ((R_A + 2R_B) × 2C) = (1/2) × f_original

So the frequency is reduced by half. (Equivalently, the period T = 1/f doubles.)

The choice claiming the frequency doubles confuses the direct relationship of period with the inverse relationship of frequency — since T grows, f must fall. The fourfold increase would only apply if C were involved as a squared term, which it is not. And the frequency cannot remain the same, because C is an active part of the timing expression and changing it necessarily changes the timing.