Amplitude modulated wave is represented by $$V_{AM} = 10\left[1 + 0.4 \cos(2\pi \times 10^4 t)\right] \cos(2\pi \times 10^7 t)$$. The total bandwidth of the amplitude modulated wave is

The amplitude modulated wave is given as: $$V_{AM} = 10\left[1 + 0.4 \cos(2\pi \times 10^4 t)\right] \cos(2\pi \times 10^7 t)$$. Comparing this with the standard AM wave equation $$V_{AM} = A_c\left[1 + \mu \cos(2\pi f_m t)\right] \cos(2\pi f_c t)$$, we identify the carrier frequency as $$f_c = 10^7$$ Hz = 10 MHz, the modulating frequency as $$f_m = 10^4$$ Hz = 10 kHz, and the modulation index as $$\mu = 0.4$$.

The bandwidth of an AM wave is given by $$\text{Bandwidth} = 2f_m$$. $$= 2 \times 10^4 \text{ Hz} = 20 \text{ kHz}$$. Hence, the correct answer is Option C (20 kHz).