a) Two waves in one string are described by the wave functions y1 = 2.90 cos (4.

Question

a) Two waves in one string are described by the wave functions y1 = 2.90 cos (4.00x - 1.40t) a) and y2 = 3.95 sin (4.85x - 2.20t) a) where y and x are in centimeters and t is in seconds. Calculate the superposition of the waves y1 + y2 at the points x = 1.15, t = 1.40. (Remember that the arguments of the trigonometric functions are in radians.) b) Calculate the superposition of the waves y1 + y2 at the points x = 1.15, t = 0.700. c) Calculate the superposition of the waves y1 + y2 at the points x = 0.575, t = 0.

Explanation / Answer

(a)y1 = 2.90 cos (4.00x - 1.40t)
At x = 1.15 cm and t = 1.40
y1 = 2.90 *cos (4.00*1.15 - 1.40*1.40) =2.896 using radian measurements .

y2 = 3.95 sin (4.85x - 2.20t)
At x = 1.15 cm and t = 1.40
y2 = 3.95 sin (4.85*1.15- 2.20*1.40) = 0.172

y1 + y2 = 2.896+ 0.172 = 3.068 cm

(b)y1 = 2.90 cos (4.00x - 1.40t)
At x = 1.15 cm and t = 0.700
y1 = 2.90 *cos (4.00*1.15 - 1.40*0.70) =2.894 using radian measurements .

y2 = 3.95 sin (4.85x - 2.20t)
At x = 1.15 cm and t = 0.70
y2 = 3.95 sin (4.85*1.15- 2.20*0.70) = 0.278

y1 + y2 = 2.894 + 0.278 = 3.172 cm

(c)y1 = 2.90 cos (4.00x - 1.40t)
At x = 0.575 cm and t = 0.00
y1 = 2.90 *cos (4.00*0.575-1.40*0) =2.897using radian measurements .

y2 = 3.95 sin (4.85x - 2.20t)
At x = 0.575 cm and t = 0.0
y2 = 3.95 sin (4.85*0.575-2.20*0) = 0.192

y1 + y2 = 2.897+ 0.192 = 3.089 cm

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