__Concept__**:**

For a DSB-full carrier wave, the transmitted power is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{\mu ^2}}}{2}} \right)\)

μ = Modulation index.

p_{c} = Carrier power.

The above expression can be written as:

\({P_t} = {P_c} + \frac{{{P_c}{\mu ^2}}}{2}\)

\(\frac{{{P_c}{\mu ^2}}}{2}\)= Sideband power.

__Analysis__**:**

For modulation index ‘μ_{1}’, the ratio of sideband to carrier power will be:

\(\frac{{{P_s}}}{{{P_c}}} = \frac{{{P_c}\mu _1^2}}{{2 \times {P_c}}} = \frac{{\mu _2^2}}{2}\) ---(1)

For μ_{2} = 2μ_{1}, the ratio will be:

\(\frac{{{P_s}}}{{{P_c}}} = \frac{{{P_c}\mu _2^2}}{{2 \times {P_c}}} = \frac{{\mu _2^2}}{2} = \frac{{4\mu _1^2}}{2}\)

\(\frac{{{P_s}}}{{{P_c}}} = 2\mu _1^2\) ---(2)

Comparing Equations (1) and (2), we conclude that **the ratio has increased by a factor of 4.**