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Two waves on one string are described by the wave functions
y1 = 2.5 cos(3.5x - 1.5t)
y2 = 3.5 sin(4.5x - 1.5t)
where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.)
(a) x = 1.00, t = 1.00
_______cm

(b) x = 1.00, t = 0.500
______cm

(c) x = 0.500, t = 0
______ cm

Respuesta :

xero099

Answer:

a) [tex]y_{R} (1.00,1.00) = -0.546\,cm[/tex], b) [tex]y_{R} (1.00,0.50) = -4.311\,cm[/tex], c) [tex]y_{R} (0.50,0.00) = 2.278\,cm[/tex]

Explanation:

The principle of superposition points out that:

[tex]y_{R}(x,t) = \Sigma^{n}_{i=1} y_{i} (x,t)[/tex]

Then, the results are:

a) [tex]y_{R} (1.00, 1.00) = y_{1} (1.00,1.00) + y_{2} (1.00,1.00)[/tex]

[tex]y_{R} (1.00,1.00) = -0.546\,cm[/tex]

b) [tex]y_{R} (1.00, 0.50) = y_{1} (1.00,0.50) + y_{2} (1.00,0.50)[/tex]

[tex]y_{R} (1.00,0.50) = -4.311\,cm[/tex]

c) [tex]y_{R} (0.50, 0.00) = y_{1} (0.50,0.00) + y_{2} (0.50,0.00)[/tex]

[tex]y_{R} (0.50,0.00) = 2.278\,cm[/tex]

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