Question

The frequency of vibrations (n) of a tunning fork depends upon length (l) of its prongs, density (S) of its material and young modulus (Y) of its material derive a formula for n using dimensions.

Answer 1

Let n = kladbyc , where k is a dimensionless constant. Substituting the dimensions of all the quantities involved, we have Comparing powers of M, L and T, we have               b + c = 0 ___________ (1)               a – 3b – c = 0 ___________ (2)               - 2c = - 1 ____________ (3) or c = ½and b = -1/2

This gives, a = - 1Therefore n = kl-1 d-1/2 y1/2
or                 
This is the required relation for the frequency of a tuning fork.