Question

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

• A. $(9+\sin (2.5\pi \times {10}^{5}t\left)\right)\sin (2\pi \times {10}^{4}t)V$
• B. $(9+\sin (4\pi \times {10}^{4}t\left)\right)\sin (5\pi \times {10}^{5}t)V$
• C. $(1+9\sin (2\pi \times {10}^{4}t\left)\right)\sin (2.5\pi \times {10}^{5}t)V$
• D. $(9+\sin (2\pi \times {10}^{4}t\left)\right)\sin (2.5\pi \times {10}^{5}t)V$

Answer 1

Answer: (D)

$(9+\sin (2\pi \times {10}^{4}t\left)\right)\sin (2.5\pi \times {10}^{5}t)V$

Analysis of graph says
$\left(1\right)$ Amplitude varies as $8-10$V or $9\pm 1$
$\left(2\right)$ Two time period as $100$ $\mu s$ (signal wave) & $8\mu s$ (carrier wave)
Hence signal is $[9\pm 1\sin \left(\frac{2\pi t}{T_1}\right)]\sin \left(\frac{2\pi t}{T_2}\right)$
$=9\pm 1\sin (2\pi \times {10}^{4}t)\sin 2.5\pi \times {10}^{5}t$.