Answer to Question #162247 in Optics for Darren

Question

Two waves on one string are described by the wave functions y1 = 3.0 cos (4.0x - 1.6t), y2 = 4.0 sin (5.0x - 2.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the points x = 1.00, t = 1.00; Remember that arguments of the trigonometric functions are in radians.

Answer 1

$$y_1(x,t)=3.0cos(4.0x-1.6t),$$ $$y_1(x=1.0,t=1.0)=3.0cos(4.0\cdot1.0-1.6\cdot1.0)=-2.2122\ cm.$$ $$y_2(x,t)=4.0sin(5.0x-2.0t),$$ $$y_2(x=1.0,t=1.0)=4.0sin(5.0\cdot1.0-2.0\cdot1.0)=0.5645\ cm.$$ $$y_1+y_2=-2.2122\ cm+0.5645\ cm=-1.6477\ cm.$$