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.
Verified Correct Answer: .
Physical Principles & Numerical Solution
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\(\sqrt{\frac{T}{\mu}}\)
Source: Myschool Past Questions Archive (Record #59509)