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Physics Question on communication systems

An amplitude modulated signal is plotted below: Which one of the following best describes the above signal ?

A

(9+sin⁡(2.5π×105  t))sin⁡(2π×104t)V(9 + \sin (2.5 \pi \times 10^5 \; t)) \sin (2\pi \times 10^4 t)V

B

(9+sin⁡(4π?104t))sin⁡(5π×105t)V(9 + \sin (4\pi ? 10^4 t)) \sin (5\pi \times 10^5t)V

C

(1+9sin⁡(2π×104t))sin⁡(2.5π?105t)V(1 + 9 \sin (2 \pi \times 10^4 t)) \sin (2.5 \pi ? 10^5t)V

D

(9+sin⁡(2π?104t))sin⁡(2.5π×105t)V(9 + \sin (2\pi ? 10^4 t)) \sin (2.5 \pi \times 10^5t)V

Answer

(9+sin⁡(2π?104t))sin⁡(2.5π×105t)V(9 + \sin (2\pi ? 10^4 t)) \sin (2.5 \pi \times 10^5t)V

Explanation

Solution

Analysis of graph says
(1) Amplitude varies as 8−10 V8 - 10\, V or 9±19 \pm 1
(2) Two time period as
100  μs100 \; \mu s (signal wave) & 8 μs8\, \mu s (carrier wave)
Hence signal is [9±1sin⁡(2πtT1)]sin⁡(2πtT2)\left[9 \pm 1 \sin\left(\frac{2\pi t}{T_{1}}\right)\right] \sin \left(\frac{2\pi t}{T_{2}}\right)
=9±1sin⁡(2π×104t)sin⁡2.5π×105  t= 9 \pm 1 \sin (2 \pi \times 10^4 t) \sin 2.5 \pi \times 10^5 \; t