The mathematical form of an AM wave is given | vedclass

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(A) The given $AM$ wave equation is $e = 50 (1 + 0.5 \sin(2\pi 	imes 5 	imes 10^{3} t)) \sin(31.4 	imes 10^{6} t)$.Comparing this with the standard

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$5 	ext{ kHz}$

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(A) The given $AM$ wave equation is $e = 50 (1 + 0.5 \sin(2\pi 	imes 5 	imes 10^{3} t)) \sin(31.4 	imes 10^{6} t)$.Comparing this with the standard form $e = E_c (1 + m_a \sin(\omega_m t)) \sin(\omega_c t)$:$1$. The carrier angular frequency is $\omega_c = 31.4 	imes 10^{6} 	ext{ rad/s}$. The carrier frequency $f_c = \frac{\omega_c}{2\pi} = \frac{31.4 	imes 10^{6}}{2 	imes 3.14} = 5 	imes 10^{6} 	ext{ Hz} = 5 	ext{ MHz}$.$2$. The modulating angular frequency is $\omega_m = 2\pi 	imes 5 	imes 10^{3} 	ext{ rad/s}$. The modulating frequency $f_m = 5 	imes 10^{3} 	ext{ Hz} = 5 	ext{ kHz}$.$3$. An $AM$ wave consists of the carrier frequency $(f_c)$,the Lower Sideband $(LSB = f_c - f_m)$,and the Upper Sideband $(USB = f_c + f_m)$.$4$. $LSB = 5 	ext{ MHz} - 5 	ext{ kHz} = 4.995 	ext{ MHz}$.$5$. $USB = 5 	ext{ MHz} + 5 	ext{ kHz} = 5.005 	ext{ MHz}$.The modulating frequency $(f_m = 5 	ext{ kHz})$ itself is not present in the final $AM$ wave spectrum; only the carrier and the sidebands are present.

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ volts}$. Which of the following frequencies is absent in the given $AM$ wave?

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