The wave speed \( (v) \) in a uniform freely hanging rope varies with the distance \( y \) from the top. The tension \( T \) varies while the mass per unit length \( \mu \) remains same. We want to design a rope in which \( v \) is independent of \( y \). For such a rope \( \mu \) cannot be constant.
Let \( \mu_{0} \) is the mass per unit length at the top of the rope \( (y=0) \). If the rope is infinitely шшш
\( P \) long and the velocity of wave is constant throughout it, then
(a) \( \mu(y)=\mu_{0} e^{\left(-\frac{g}{v^{2}} \cdot y\right)} \)
(b) \( \mu(y)=\frac{\mu_{0}}{2} e^{\left(-\frac{g}{v^{2}} \cdot y\right)} \)
(c) \( \mu(y)=\frac{\mu_{0}}{2} e^{\left(-\frac{2 g}{v^{2}} \cdot y\right)} \)
(d) \( \mu(y)=\mu_{0} e^{\left(-\frac{g}{2 v^{2}} \cdot y\right)} \)
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