Question

Assuming that the frequency gamma of a vibrating string may depend upon 1.applied force 2.length 3.mass per unit ,prove that gamma alpha 1/l root of f/m using dimensional analysis

Answer 1

Answer:

Explanation:

dimension of frequency = [T⁻¹]

Dimension of applied force , F = [MLT⁻²]

dimension of length , l = [L]

dimension of mass per unit length, m = [ML⁻¹]

Now suppose , frequency = F^x L^y m^z

So, [T⁻¹] = [MLT⁻²]^x [L]^y [ML⁻¹]^z

[T⁻¹] = [M]^(x + z) [L]^(x + y - z) [T]^(-2x)

compare both sides,

x + z = 0

x + y - z = 0

-2x = -1 ⇒x = 1/2

So, z = -1/2 and y = -1

Hence, frequency is directly proportional to 1/l √(F/m}