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
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