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A wave pulse starts propagating in +x-direction along a non-uniform wire of length L witdt mass per unit length given mu=m_(0)+alpha x and under tension of TN. Find the time taken by the pulse to travel from the lighter end (x = 0) to the heavier end. |
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Answer» SOLUTION :VELOCITY oftransverse wave in a STRING. `v = (dx)/(dt) = sqrt(T/m) = sqrt(T/(m_0 + alphax))` `:. sqrt(m_0 + alphax) dx= sqrtT dt` Integrating within proper limits, `int_0^L sqrt(m_0 + alpha x) dx = sqrtT int_0^t dt` `RARR [(2(m_0 + alphax)^(3//2))/(3alpha)]_0^L = sqrtTt` `:. t = 2/(3 alpha sqrtT) [(m_0 + alphaL)^(3//2) -m_0^(3//2)]` |
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