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Q.

Following is given the equation of a stationary wave (all in SI units)  y = (0.06)sin(2πx) cos(5πt)
Match the following

 Table 1 Table-2
A)Amplitude of constituent waveP)0.06
B)Position of node at x =……mq)0.5
C)Position of antinode at x =….mR)0.25
D)Amplitude at x = 3/4mS)0.03
 ABCD
1)SRQP
2)RSPQ
3)SRPQ
4)RSQP

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a

2

b

1

c

3

d

4

answer is A.

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Detailed Solution

detailed_solution_thumbnail

(A) Amplitude of constituent wave
= maximum amplitude of stationary wave/2
= 0.03m
(B) 0.06sin2πx
At node, Ax = 0
2πx = 0, π, 2π...... 
x = 0, 0.5, 1.0, ...(in m)
(C) In between the nodes, there are antinodes. Therefore there are antinodes at x = 0.25m, 0.75m…. 
(D) At x = 3/4m or 0.75m, we are getting antinode or Ax = 0.06m

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