In amplitude modulation, the message signal V _ m ( t ) = 10 (2π ×...

In amplitude modulation, the message signal ${V}_{m}( t ) = 10\sin \left(2\pi \times {10}^{5}t\right)$ volts and carrier signal ${V}_{C}\left(t\right) = 20\sin \left(2\pi \times {10}^{7}t\right)$ volts. The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is $\alpha kHz$. The value of $\alpha$ is: