An amplitude modulated signal is given by $$V(t) = 10[1 + 0.3 \cos(2.2 \times 10^4 t)] \sin(5.5 \times 10^5 t)$$. Here t is in seconds. The sideband frequencies (in kHz) are, [Given $$\pi = 22/7$$]

$$\text{The given expression is: } V(t) = 10\left[1 + 0.3 \cos\left(2.2 \times 10^4 t\right)\right] \sin\left(5.5 \times 10^5 t\right)$$

$$\text{Comparing with standard AM equation: } V(t) = A_c [1 + \mu \cos(\omega_m t)] \sin(\omega_c t)$$

$$\omega_m = 2.2 \times 10^4\text{ rad/s} \implies f_m = \frac{\omega_m}{2\pi} = \frac{2.2 \times 10^4}{2 \times \frac{22}{7}} = \frac{2.2 \times 10^4 \times 7}{44} = 3500\text{ Hz} = 3.5\text{ kHz}$$

$$\omega_c = 5.5 \times 10^5\text{ rad/s} \implies f_c = \frac{\omega_c}{2\pi} = \frac{5.5 \times 10^5}{2 \times \frac{22}{7}} = \frac{5.5 \times 10^5 \times 7}{44} = 87500\text{ Hz} = 87.5\text{ kHz}$$

$$\text{Upper Sideband Frequency (USB): } f_{\text{USB}} = f_c + f_m = 87.5 + 3.5 = 91.0\text{ kHz}$$

$$\text{Lower Sideband Frequency (LSB): } f_{\text{LSB}} = f_c - f_m = 87.5 - 3.5 = 84.0\text{ kHz}$$