In Amplitude Modulation, the message signal \( V_m(t) = 10 \sin(2\pi \times 10^{5} t) \) volts and carrier signal \( V_c(t) = 20 \sin(2\pi \times 10^{7} t) \) volts. The modulates signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is \( a \) kHz. The value of \( a \) is:
