A carrier signal $$C(t) = 25\sin(2.512 \times 10^{10}t)$$ is amplitude modulated by a message signal $$m(t) = 5\sin(1.57 \times 10^{8}t)$$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

The message signal is $$m(t) = 5\sin(1.57 \times 10^8 \, t)$$. The angular frequency of the message signal is $$\omega_m = 1.57 \times 10^8$$ rad s$$^{-1}$$, so the frequency of the message signal is $$f_m = \frac{\omega_m}{2\pi} = \frac{1.57 \times 10^8}{2\pi} = \frac{1.57 \times 10^8}{6.284} \approx 2.5 \times 10^7$$ Hz $$= 25$$ MHz.

In amplitude modulation, the bandwidth is twice the frequency of the message signal: $$\text{Bandwidth} = 2f_m = 2 \times 25 = 50$$ MHz.