Using dimensional analysis obtain an expression for the speed of transverse waves in a stretched string.

Explanation

Wave velocity `v prop T^(a) mu ^(b) implies V =KT^(a) mu ^(b) rarr ` (1)
Dimensions of `v = M^(0)L^(1) T^(-1) `, Tension `= M^(1) L^(1) T^(-2)` ,
Linear mass ` mu = M^(1) L^(-1) `, Constant `K = M^(0) L^(0) T^(0) `
Now (1) becomes `M^(0) L^(1) T^(-1)= [M^(1) L^(1) T^(-2) ] ^(a) [M^(1) L^(-1) ]^(b)`
` M^(0) L^(1) T^(1) = M^(a+b) L^(a-b) T^(-2a)` ltbgt Comparing the powers of same physical quantity
`-1 = -2a implies a = (1)/(2)`
`a+b =0 implies b= - (1)/(2)`
`implies v = (1) =T^((1)/(2)) mu ^((1)/(2)) ` `[ :' K = 1`Practically]
` :. mu = sqrt((T)/(mu))`