Question

An amplitude-modulated wave is represented by, $C_m=10(1+0.2\sin 12560t)\sin (1.11\times {10}^{4}t)V$, the modulating frequency in $kHz$ will be

Answer 1

Step 1. Given data:

An amplitude-modulated wave $=C_m=10(1+0.2\sin 12560t)\sin (1.11\times {10}^{4}t)V..........\left(1\right)$

Step 2. Formula used:

In general,

An amplitude-modulated wave $=C_m=A_c(1+\frac{A_m}{A_c}\sin {\omega }_{m}t)\sin {\omega }_{c}tV..........\left(2\right)$

where, $A_m$is the Amplitude of modulating wave in $m$

$A_c$is the Amplitude of carrier wave in $m$

$\sin {\omega }_{m}t$and $\sin {\omega }_{c}t$ is the phase of modulating wave and carrier wave respectively.

Step 3. Find the modulating frequency:

By comparing equations $\left(1\right)$and $\left(2\right)$, we get

${\omega }_m=12560rad/sec$

$f_m=\frac{{\omega }_m}{2\pi }Hz\{\because {\omega }_m=2{\mathrm{\pi f}}_{\mathrm{m}}\}$

where, $f_m$ is the frequency of modulation

$f_m=\frac{12560}{2\times {\displaystyle 3.14}}Hz\{Assume\mathrm{\pi }=3.14\}$

$f_m=2000Hz=2kHz$

Hence, modulating frequency is $2kHz$.