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Question

y(x,t)=0.8/[(4x+5t)2+5] represents a moving pulse, where x and y are in meter and t in second. Then

A
pulse is moving in +x direction
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B
in 2s it will travel a distance of 2.5 m
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C
its maximum displacement is 0.16 m
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D
it is symmetric pulse
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Solution

The correct options are
B in 2s it will travel a distance of 2.5 m
C its maximum displacement is 0.16 m

The maximum displacement is the maximum value of y(x,t)

y(x,t)=0.8(4x+5t)2+5

For y to be maximum, denominator of the expression must be minimum. Which means when (4x+5t)=0

then

y=0.85=0.16m

Option C is correct

Now we know that wave equation is given by

d2y(x,t)dt2=c2d2y(x,t)dx2

now using differentiation we get

d2y(x,t)dt2=160(4x+5t)2{(4x+5t)2+5}340{(4x+5t)2+5}3=25⎢ ⎢6.4(4x+5t)2{(4x+5t)2+5}31.6{(4x+5t)2+5}3⎥ ⎥

and

d2y(x,t)dx2=16⎢ ⎢6.4(4x+5t)2{(4x+5t)2+5}31.6{(4x+5t)2+5}3⎥ ⎥C=2516=54m/sec

So in 2 seconds it will travel distance =2C=2.5m

Since f(x,t)f(x,t) the pulse is not symmetric


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