# An audio frequency of $4\times 10^3$Hz is used to modulate a carrier wave of frequency 1MHz.The band width is

$\begin{array}{1 1}(a)\;4\times 10^3Hz\\(b)\; 4\times 10^6Hz\\(c)\;8\times 10^3Hz\\(d)\;8\times 10^6Hz\end{array}$

Carrier wave frequency $f_c=10^6Hz$
Signal wave frequency $f_s=4\times 10^3$Hz
Frequencies of side band $f_1=f_c+f_s$
$\Rightarrow 10^6+4\times 10^3$
$\Rightarrow 1.004\times 10^6$Hz
$f_2=f_c-f_s$
$\;\;\;\;=10^6-4\times 10^3$
$\;\;\;\;=0.996\times 10^6Hz$
Band width=$f_2-f_1$
$\Rightarrow 1.004\times 10^6-0.996\times 10^6$
$\Rightarrow 8\times 10^3$Hz
Hence (c) is the correct option.