The velocity v, of a wave in a stretched string, depends on the tension T,...

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\(\sqrt{\frac{T}{\mu}}\)