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

Match List-I with List-II

We do not transmit low frequency signal to long distances because-

(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.

(b) Effective power radiated by a long wavelength baseband signal would be high.

(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously.

(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well.

Therefore, the most suitable option will be :

A sinusoidal wave y(t) = 40sin(10 $$\times$$ 10⁶ $$\pi$$t) is amplitude modulated by another sinusoidal wave x(t) = 20sin (1000 $$\pi$$t). The amplitude of minimum frequency component of modulated signal is :