The antenna current of an AM broadcast transmitter, modulated to depth of 40% by an audio sine wave is 11 A. It increases to 12 A. as a result of simultaneous modulation by another audio sine wave. What is the modulation index due to this 2nd wave?

$I_t1=11 A ,M1=0.4,I_t2=12 A$

Find mod index due to 2nd wave

$-\big[\frac{I_{t1}}{I_c} \big]^2=1+\frac{m_1^2}{2} \\ ∴I_c=\frac{I_t}{\big[1+\frac{m^2}{2}\big]^\frac{1}{2}} =10.58 A \\ I_{t2}^2=I_c^2 \big[1+\frac{m^2}{2}\big] \\ m_t=0.756 \\ m_t=[m_1^2+m_2^2 ]^\frac{1}{2} \\ =[m_t^2-m_1^2 ]^\frac{1}{2}=[(0.756)^2-(0.4)^2 ]^\frac{1}{2} \\ m_2=0.6415 \\ =64.15\% $