Question

the frequency f of a tuning fork depends on the length of an arm l,density of the material p and the youngs modulus y.obtain a relation between the above quantities by usind dimensional analysis

Answer 1

freq  f  =  [T]⁻¹
length of the arm L = [L]
density ρ =   [ M ] [ L ]^⁻³ 
Young's modulus =  Y = [M] [L⁻¹] [T ]⁻² 

let     f =  L^a  ρ^b  Y^c
     so      a - 3b - c = 0
               b  + c = 0
               C = 1/2
    => b = -1/2       a = -1
 
       f =   1/L *  √[(Y/ρ)
 

Answer 2

Answer:

$n \: = \frac{k}{l} \frac{ \sqrt{y} }{ \sqrt{d} }$