The mathematical form of an AM wave is given | vedclass

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(B) The standard equation for an $AM$ wave is $e = E_c (1 + m_a \sin(\omega_m t)) \sin(\omega_c t)$.Comparing the given equation $e = 50 (1 + 0.5 \sin

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$5 	ext{ MHz}, 5 	ext{ kHz}$

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(B) The standard equation for an $AM$ wave is $e = E_c (1 + m_a \sin(\omega_m t)) \sin(\omega_c t)$.Comparing the given equation $e = 50 (1 + 0.5 \sin(2\pi 	imes 5 	imes 10^{3} t)) \sin(31.4 	imes 10^{6} t)$ with the standard form:The angular frequency of the modulating signal is $\omega_m = 2\pi 	imes 5 	imes 10^{3} 	ext{ rad/s}$.The modulating frequency is $f_m = \frac{\omega_m}{2\pi} = \frac{2\pi 	imes 5 	imes 10^{3}}{2\pi} = 5 	imes 10^{3} 	ext{ Hz} = 5 	ext{ kHz}$.The angular frequency of the carrier wave is $\omega_c = 31.4 	imes 10^{6} 	ext{ rad/s}$.The carrier frequency is $f_c = \frac{\omega_c}{2\pi} = \frac{31.4 	imes 10^{6}}{2 	imes 3.14} = \frac{31.4 	imes 10^{6}}{6.28} = 5 	imes 10^{6} 	ext{ Hz} = 5 	ext{ MHz}$.

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ V}$. For the given $AM$ wave,the carrier frequency is ....... and the modulating frequency is .......

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