check the dimensional accuracy of n=1/2L*rootT/M

Asked by gopikagopakumar43 | 13th Dec, 2020, 12:56: PM

Expert Answer:

I guess the equation is 
begin mathsize 14px style n space equals space fraction numerator 1 over denominator 2 L end fraction square root of T over mu end root end style ................  (1)
where n is frequency of transverse wave, L is length of string that forms stationary waves . 
T is tension in the string and μ is linear mass density i.e., mass per unit length
Dimension of T = [ M L T -2 ]
Dimension of μ = [ M L-1 ]
Hence, dimension of square root of T over mu end root = L T-1
Dimension of RHS of eqn.(1) =  L-1 L T -1 = T-1 
In LHS of eqn.(1), we have frequency that hs dimension T -1
Hence dimension of LHS and RHS of eqn.(1) is matching exactly

Answered by Thiyagarajan K | 14th Dec, 2020, 12:38: AM