A certain AM transmitter is radiating 125 kW when a certain audio sine wave is modulating it to a depth of 70% and 144.5 kW when a second sinusoidal audio wave also modulates it simul-taneously. What is the depth of the modulation for the second audio wave?

Given that,

Total transmitted power (p_t1) = 125kW

Modulation index (m_a1) = 70%

P_t2 = 144.5kW

m_a2 = ?

p_t = p_c \([1+\frac{m^2_a1}{2}]\)

P_c = \(\frac{125\times 10^3}{1+\frac{(0.70)^2}{2}}= 100.40kW\)

P_c = Power of the carrier signal.

P_t = P_c \([1+\frac{m^2_a1}{2}]= 144.5\times 10^3 = 100.4\times10^3[1+\frac{m^2_a1}{2}]\)

m²_at = 0.878 

m²_at = m²_a1 + m²_a2 

m_a2 = \(\sqrt 0.388\) = \(\sqrt 0.4\)

Here, option 1 is correct.