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

ID: 1488330 • Letter: T

Question

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

y1 = 1.00 sin (x + 0.500t)

y2 = 1.00 sin (x 0.500t)

where x, y1, and y2 are in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at the following positions

. (a) x = 0.150 cm

|ymax| = ???cm

(b) x = 0.460 cm

|ymax| = ???cm

(c) x = 1.40 cm

|ymax| = ???cm

(d) Find the three smallest values of x corresponding to antinodes. (Enter your answers from smallest to largest.)(in cm)

Explanation / Answer

y1 = 1.00 sin (x + 0.500t)

y2 = 1.00 sin (x 0.500t)

Using the following equation

sin (a) + sin (b) = 2 * sin(a+b)/2 * cos (a-b)/2

Y = Y1 + Y2

Y = 2 sin (pi* x) cos (.5t*pi)

a) At x = .150 cm

Y max is 0.9 cm

b) x= .46

y max = 1.98cm

c) x =1.4
Y max = 1.9 cm (negative)

d) For finding the smallest value of X for the antinodes , it should begin from the origin.

Hence x =.5,1.5,2.5 cm