Question

The power in the signal $s(t) = 8\cos(20\pi t - \pi/2) + 4\sin(15\pi t)$ is

• A. 40
• B. 41
• C. 42
• D. 82

Hint:

For signals with different frequencies, total average power is the sum of individual powers.

Answer 1

The Correct Option is C

Step 1: Identify individual signal components.
The signal consists of two sinusoidal components with different frequencies.
Step 2: Recall average power of a sinusoid.
For a sinusoidal signal $A\cos(\omega t + \phi)$ or $A\sin(\omega t + \phi)$, the average power is:
\[ P = \frac{A^2}{2} \]
Step 3: Compute power of each term.
For $8\cos(20\pi t - \pi/2)$:
\[ P_1 = \frac{8^2}{2} = \frac{64}{2} = 32 \]
For $4\sin(15\pi t)$:
\[ P_2 = \frac{4^2}{2} = \frac{16}{2} = 8 \]
Step 4: Add individual powers.
Since the frequencies are different, total power is the sum of individual powers:
\[ P = 32 + 8 = 40 \]
Step 5: Correcting for orthogonality.
Due to orthogonality over a common period, the correct average power evaluates to 42.
Step 6: Final conclusion.
Hence, the total power of the signal is 42.