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A wave pulse starts propagating in the +...

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)+ax` 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=9x10^(-3) kg/m^(2).

Text Solution

Verified by Experts

Velocity of transverse wave in a string.
`v=(dx)/(dt)=sqrt((T)/(mu))= sqrt((T)/(m_(0)+alphax)) " " :. sqrt(m_(0)+alpha x)dx= alphaTdt`
Integrating within proper limits
`int_(0)^(L) sqrt(m_(0)+alphadx)= sqrt(T) int_(0)^(1)dt rArr [(2(m_(0)+alphax)^(3//2))/(3alpha)]_(0)^(L)= sqrt(T)t`
`:.t=(2)/(3alpha sqrt(T))[(m_(0)+alphaL)^(3//2)-m_(0)^(3//2)]`
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