An amplitude modulated wave is represented by $C_{m}(t)=10(1+0.2 \cos 12560 t) \sin \left(111 \times 10^{4} t\right)$ volts. The modulating frequency in kHz will be .......

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Semiconductors

An amplitude modulated wave is represented by

C_{m} (t) = 10 (1 + 0.2 cos 12560 t) sin (111 \times 1 0^{4} t)

volts.
The modulating frequency in kHz will be .......

Answer: 2

The general form of an AM wave is

C_{m} (t) = A_{c} (1 + m cos ω_{m} t) sin ω_{c} t

, where

ω_{m}

is the angular frequency of the modulating signal. Comparing with the given equation:

ω_{m} = 12560

rad/s. The modulating frequency is

f_{m} = \frac{ω _{m}}{2 π} = \frac{12560}{2 π} \approx 2000

Hz = 2 kHz.

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Integer answer