Two transverse sinusoidal waves combining in a medium are described by the wave

Question

Two transverse sinusoidal waves combining in a medium are described by the wave functions y_1 = 5.00 sin n(x + 0.5001) Y_2 = 5.00 sin n(x - 0.5001) where x, y_1 and y_2 are in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at the following the displacement of the medium at any particular position and time is given by the sum of the displacements due to Find the three smallest values of x corresponding to antinodes. (Enter your answers from smallest to largest.)

Explanation / Answer

y= 5.00 sin (x + 0.500t) = 5 {sin x*cos 0.500t + cosx*sin 0.500t}
y= 5.00 sin (x - 0.500t),= 5 {sin x*cos 0.500t - cosx*sin 0.500t}

y1 + y2 = 10 (sin x)*(cos 0.500t )
For the maximum value (cos 0.500t ) = 1

a) At x = 0.19
10* (sin x)* = 5.62 cm

b) At x = 0.62
10* (sin x)* = 9.3 cm

c) At x = 1.4
-10* (sin x)* = 9.51 cm

d) y1 + y2 = 10 (sin x)*(cos 0.500t)

At anti nodes cos 0.500t = 1
y1 + y2 = 10 (sin x)*1
sin x is the maximum when
x = 1/2, 3/2 , 5/2

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