Wave Motion 2 Question 32

32. The (x,y) coordinates of the corners of a square plate are (0,0),(L,0),,(L,L) and (0,L). The edges of the plate are clamped and transverse standing waves are set-up in it. If u(x,y) denotes the displacement of the plate at the point (x,y) at some instant of time, the possible expression (s) for u is (are) (a= positive constant )

(1998, 2M)

(a) acos(πx/2L)cos(πy/2L)

(b) asin(πx/L)sin(πy/L)

(c) asin(πx/L)sin(2πy/L)

(d) acos(2πx/L)sin(πy/L)

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Answer:

Correct Answer: 32. (b,c)

Solution:

  1. Since, the edges are clamped, displacement of the edges u(x,y)=0 for

Line,

OA i.e. y=00xLAB i.e. x=L0yLBC i.e. y=L0xLOC i.e. x=00yL

The above conditions are satisfied only in alternatives (b) and (c).

Note that u(x,y)=0, for all four values eg, in alternative (d), u(x,y)=0 for y=0,y=L but it is not zero for x=0 or x=L. Similarly, in option (a) u(x,y)=0 at x=L,y=L but it is not zero for x=0 or y=0 while in options (b) and (c), u(x,y)=0 for x=0,y=0x=L and y=L.



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