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Assuming that the period of vibration of a tunning fork depends upon the length l of the prong and on the density and Young's modulus y of the material.Find the method of dimensions,a formula for the period of vibration

Let n = kl^ad^by^c , 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 = ½

This gives, a = - 1

This is the required relation for the frequency of a tuning fork.