Assuming that the frequency `gamma` of a vibrating string may depend upon (i) applied force (F) (ii) length (l) (iii) mass per unit lengt (m), prove that `gamma prop1/l sqrt(F/m)` using dimensional analysis.

Explanation

1. This method gives no information about the dimensionless constants in the formula like 1,2,…. `pi ` etc .
2. This method cannot decide whether the given quantity is a vector or a scalar .
3. This method is not suitable to derive relations involing trigonimetric , exponential and logarihmic function .
4. It cannot be applied to an equation involving more than three physical exponentites
5. It can only check on whether a physical relation is dimensionally correct but not the correctness of the relation . FOr example , using dimensional analysis `, s= u t + 1/3 at^2 ` is dimensionally correct whereas the correct relation is `s = u t +1/2 at ^2`
(ii ) ` n prop I^(a) T^(b ) m^(c) , [1] = [ M^0 L^1 T^0 ]`
` [T] = [ M^(1) L^(1) T^(-2) ] ( " force")`
` [m] = [M^(1) L^(-1) T^(0)]`
`[M^(0 ) L^(0) T^(-1) ] = [ M^(0) L^(1) T^(0)]^(a) [M^1 L^(1 ) T^(-2)]^(b) [M^(0 ) L^(-1) T^0 ]`.
` b+ c =0`
` a-b -c =0`
`-2b =- 1 implies =1/2`
` C=- 1/2 a=1`
` gamma prop 1/l sqrt((T)/(m))`