In an amplitude modulation, a modulating signal having amplitude of $X \mathrm {~V}$ is superimposed with a carrier signal of amplitude $Y \mathrm {~V}$ in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude $2Y \mathrm {~V}$. The ratio of modulation index in the two case respectively will be :\\
(1) $1 : 2$\\
(2) $1 : 1$\\
(3) $2 : 1$\\
(4) $4 : 1$