Chapter 13.3, Problem 7CYU

a)

To determine

To Calculate: Sum of given functions.

Answer to Problem 7CYU

0

Explanation of Solution

Given information:

We know that, the given expression is two functions are given

Formula used:

Signs of trigonometric ratios in different quadrants

Calculation:

For first signal, $y=20\sin (3\theta +{45}^{\circ })\mathrm{.....}(1)$

For second signal, $y=20\sin (3\theta +{225}^{\circ })$

  $\begin{array}{l}=20\sin (3\theta +{45}^{\circ }+{180}^{\circ })\\ y=-20\sin (3\theta +{45}^{\circ })\text{as}\sin ({180}^{\circ }+\theta )=-\sin \theta \end{array}$

Addition equation (1) to this function,

  $\begin{array}{l}2y=0\\ \therefore y=0\end{array}$

b)

To determine

To Calculate: To identify type of interference

Answer to Problem 7CYU

destructive

Explanation of Solution

Given information:

We know that, sum of the two functions.

Formula used:

Definition of destructive interference

Calculation:

Follows by definition of destructive interference