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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

1 Answer

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Final answer:

The superposition of the waves y1 + y2 at different points is found by adding the wave functions together at each point.

Step-by-step explanation:

To find the superposition of the waves y1 + y2, we simply add the two wave functions together at each given point.

(a) At x = 1.00 cm and t = 1.00 s:

y1 + y2 = 2.5 cos(3.5(1.00) - 1.5(1.00)) + 3.5 sin(4.5(1.00) - 1.5(1.00))

= 1.78 cm

(b) At x = 1.00 cm and t = 0.500 s:

y1 + y2 = 2.5 cos(3.5(1.00) - 1.5(0.500)) + 3.5 sin(4.5(1.00) - 1.5(0.500))

= 1.08 cm

(c) At x = 0.500 cm and t = 0:

y1 + y2 = 2.5 cos(3.5(0.500) - 1.5(0)) + 3.5 sin(4.5(0.500) - 1.5(0))

= 2.5 cm

User Ahmet Firat Keler
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