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Question

# You have learnt that a travelling wave in one dimension is represented by a function y= f(x, t) w ere x must appear in the combination x Vt or x + vt, i.e. y = F(x±vt) Is the converse true? Examine if the following function for y can possibly represent a travelling wave :

A
(xvt)2
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B
log[(x+vt)/x0]
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C
exp[(x+vt)/x0]
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D
none of these
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Solution

## The correct option is D none of theseThe is not true, means f any function representing in the form of y=f(x±vt) it doesn't necessarily express a travelling wave.The essential condition is that if any function y=f(x±vt) satisfiedd2y/dt2=v2d2y/dx2(a) It's wave equation,y=(x−vt)2dy/dt=−2v(x−vt)dy/dt=2v2Againdy/dx=2(x−vt)d2y/dt2=v2.d2y/dx2Hence, it's wave equation(b)log [(x+vt)/xo]It's not wave equations because it doesn't follow d2y/dt2=v2.d2y/dx2Also at x=0 and t=0Log(0)→∞ infiniteHence, it's not wave equation(c) 1/(x+vt)It's not wave equation,d2y/dt2=v2.d2y/dx2

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