$1\mathrm{.}8$ Two waves on a string are given by the functions:

$y_1(x,t)=4cos(20t-30x),(cm)$

$y_2(x,t)=-4cos(20t+30x),(cm),$

where $x$ is in centimeters. The waves are said to interfere

constructively when their superposition $|y_s|=|y_1+y_2|$ is a

maximum, and they interfere destructively when $|y_s|$ is a

minimum.

$($a$)$ What are the directions of propagation of waves $y_1(x,t)$

and $y_2(x,t)?$

$($b$)$ At $t=(\frac{}{50})s,$ what location $x$ do the two waves

interfere constructively, and what is the corresponding

value of $|y_s|?$

$($c$)$ At $t=(\frac{}{50})s,$ what location $x$ do the two waves

interfere destructively, and what is the corresponding

value of $|y_s|?$