Question

An amplitude-modulated wave is represented by C_m(t) = 10(1 + 0.2 cos 12560t) × sin (111 × 10⁴t) volts. The modulating frequency in kHz will be ______.

Options

• 1kHz

• 2kHz

• 3kHz

• 4kHz

Answer 1

An amplitude-modulated wave is represented by C_m(t) = 10(1 + 0.2 cos 12560t) × sin (111 × 10⁴t) volts. The modulating frequency in kHz will be 2kHz.

Explanation:

When we compare the given amplitude-modulated wave equation to a standard equation, we get;

`C_m = A_c(1 + (A_m)/(A_c)cos2xf_mt)sin2pif_ct`

Given: C_m = 10(1 + 0.2 cos 12560t) sin(111 × 10⁴t)

So, cos2πf_mt = cos 12560t

⇒ 2πf_m = 12560

⇒ `f_m = 12560/(2 xx 3.14) = 2000` = 2kHz