A wave pulse starts propagating in the +x-direction along a non-uniform wire of length 10 m with mass per unit length given by `mu=mu_(0)+az` and under a tension of 100 N. find the time taken by a pulse to travel from the lighter end (x=0) to the heavier end. `(mu_(0)=10^(2) kg//m and a=9xx10^(-3)kg//m^(2)).

A wave pulse starts propagating in the +x-direction along a non-unifor

1.	A wave pulse starts propagating in the +x-direction along a non-uniform wire of length 10 m with mass per unit length given by `mu=mu_(0)+az` and under a tension of 100 N. find the time taken by a pulse to travel from the lighter end (x=0) to the heavier end. `(mu_(0)=10^(2) kg//m and a=9xx10^(-3)kg//m^(2)).
Answer» The speed of the wave pulse `v=sqrt(T)/(mu)=sqrt((T)/(mu_(0)+ax)=(dx)/((dt)` `:. T=int_(0)^(t) dt=int_(0)^(L) sqrt((mu_(0)+ax)/(T) )dx=(2)/(3)(1)/(asqrt(T))[(mu_(0)+aL)^(3//2)-(mu_(0))^(3//2)]` substituting the value, we get `t=(2)/(3)xx(1)/(9xx10^(-3)xxsqrt(100))[(10^(-2)+9xx10^(-3)xx102))(3//2)-(10^(-2)^(3//2]` `=(2xx100)/(27)[(10)^(-3//2)-(10)(-3)]=0.227 s`

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