The velocity v, of a wave in a stretched string, depends on the tension T, in the spring and the mass per unit length of the spring. Obtain an expression for v in terms of T and u, using the method of dimensions.
Explanation
Expression for v c = kT\(^a\)U\(^b\), k is dimensionless [v] = k[T]\(^a\)[\(\mu\)]\(^b\) Lt\(^{-1}\) = kM\(^{a \div b}\) L\(^{a + b}\) T\(^{-2a}\) For T, -1 = 2a a = \(\frac{1}{2}\) For M, 0 = a + b b = -a = \(\frac{1}{2}\) v = KT\(^{\frac{1}{2}}\)\(\mu^{- \frac{1}{2}}\) OR v = k\(\sqrt{\frac{T}{\mu}}\)
