Question

The average value of a double-frequency sinusoid, $\mathbf{sin}\left(2\mathrm{\omega t}+\delta \right)$, is given by

(a) 1

(b) $\mathbf{\delta }$

(c) zero

Short answer

Answer

The correct option is (c); tha is, zero.

Step-by-step solution

Define the average value of a waveform

The average value of a a wave form is the area intercepted by the sine wave signal in one cycle.

Use the area traversed by a sinusoidal waveform

The area intercepted in the first half of the cycle is equal to the area intercepted in the negative half cycle.Since the positive and the negative cycles of the sinsoid cancels each other, the average power is zero.

Therefore, the average value of the sinusoidal waveform is zero. Thus, Option (c) is correct.

Explanation for Option (a)

The average value of the sinusoidal waveform is zero. However, the average power in Option (a) is a 1. Therefore, it is an incorrect option.

Explanation for Option (b)

The average value of the sinusoidal waveform is zero. However, the average power Option (b) provides is $\delta$. Moreover, the average value of a sinusoidal waveform is always independent of the frequency of a signal. Thus, Option (b) is incorrect.