Two waves are propagating on the same very long string. A generator on the right
ID: 2015536 • Letter: T
Question
Two waves are propagating on the same very long string. A generator on the right end creates a wave given by
y=(3.48 cm)cos[(/2)((2.16 m-1)x+(10.24 s-1)t)],
while one at the left end creates the wave given by
y=(3.48 cm)cos[(/2)((2.16 m-1)x-(10.24 s-1)t)].
a) Find the coordinate x>0 of the point closest to the origin on the positive x-axis such that there is no motion (a node). b) Find the coordinate x>0 of the point closest to the origin on the positive x-axis such that the motion of the string reaches a maximum (an antinode). Also, c) What is the total y-displacement at x=0.058 m and t=324 s?
Explanation / Answer
nodes where cosine funtion is zero or equal to n + /2 then /2 ( 2.16 m-1 x ) = n + /2 ( 1.068 ) x = ( n+ 1/2) x = ( n+ 1/2)/ ( 1.068 ) when n = 0 = 0.468 , , 1.404, 2.34 ...... anti nodes occure inbeteen these ( 1.068) x = n x = n/ 1.068 0 , 0.936, 1.87 ........ c) adding two waves y1 + y2 y=(3.48 cm)cos[(/2)((2.16 m-1)x+(10.24 s-1)t)],+(3.48 cm)cos[(/2)((2.16 m-1)x-(10.24 s-1)t)]. y = 6.96 cos /2 (4.32 m-1 x + 20.48 s-1 t /2) y = 6.96 cm cos /2 ( 2.16 m-1 x + 10.24 s-1 t) put x=0.058 m and t=324 s y = - 6.83 cm y=(3.48 cm)cos[(/2)((2.16 m-1)x+(10.24 s-1)t)],+(3.48 cm)cos[(/2)((2.16 m-1)x-(10.24 s-1)t)]. y = 6.96 cos /2 (4.32 m-1 x + 20.48 s-1 t /2) y = 6.96 cm cos /2 ( 2.16 m-1 x + 10.24 s-1 t) put x=0.058 m and t=324 s y = - 6.83 cm y = 6.96 cos /2 (4.32 m-1 x + 20.48 s-1 t /2) y = 6.96 cm cos /2 ( 2.16 m-1 x + 10.24 s-1 t) put x=0.058 m and t=324 s y = - 6.83 cmRelated Questions
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