# An audio signal $20\sin(2\pi\times 400t)$ is used to modulating a carrier wave given by $40\sin(2\pi\times 40000t)$.The percentage modulation is

$\begin{array}{1 1}(a)\;25\%\\(b)\; 40\%\\(c)\;10\%\\(d)\;50\%\end{array}$

Amplitude of signal wave $E_s=20$
Amplitude of carrier wave $E_c=40$
Modulation index=$\large\frac{E_s}{E_c}$$\times 100 \Rightarrow \large\frac{20}{40}$$\times 100$
$\Rightarrow 50\%$
Hence (d) is the correct answer.