Q.

A triangle wave pulse on a taut string travels in positive x–direction with speed v. the tension in the string is F, and linear mass density of string is  μ. At t = 0 the shape of pulse is given by

y(x,0)=0 if  x<Lh(L+x)L for L<x<0h(Lx)L for 0<x<L0 for x>L

Choose the INCORRECT statement(s). (h << L)

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a

Magnitude of instantaneous power is zero for -L<(x-vt)<-L

b

Magnitude of instantaneous power is FvhL2 for (x – vt) > L

c

Magnitude of instantaneous power is FvhL2 for 0 < (x – vt) < L

d

Magnitude of instantaneous power is FvhL2 for (x – vt) < – L

answer is A, B, C.

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Detailed Solution

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Wave moves in positive x direction replace x by x-vt to get yx,t 

y(x,t)=0 if  x-vt<Lh(L+x-vt)L for L<x-vt<0h(Lx-vt)L for 0<x-vt<L0 for x-vt>L

Power=P(x,t)=-Fyxyt

P(x,t)=-F00=0 if  x-vt<L-FhL-hvL=FvhL2 for L<x-vt<0-F-hLhvL=FvhL2 for 0<x-vt<L-F00=0 for x-vt>L

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