Specific impulse is not affected by the number of boosters or engines on a rocket, correct? Let's say I take a rocket with two SRBs and add to more for the first stage. The specific impulse of the rocket doesn't change, right? I know for determining the specific impulse of specific stage we use the following equation
$I_{sp-eff} = \frac{I_{sp-1}\dot{m_{1}} + I_{sp_2}\dot{m_{2}}+...}{\dot{m_{1}}+\dot{m_{2}}+...} $
but adding or subtracting the same booster doesn't affect this. Specific impulse isn't directly proportional to the number of boosters, right?
The effects of changing the number of boosters would be found in the last part of the rocket equation
$\Delta{v} = v_{e} ln\frac{m_{0}}{m_{f}}$
as in, the difference in the propellant mass at the beginning of the stage and at the end of the stage would be the sole indicator that more thrust has been supplied to the rocket by the addition of two more SRBs. Correct?
