Question

Assuming that the frequency γ of a vibrating string may depend upon i) applied force (F) ii) length (A) iii) mass per unit length (m), prove that γα

Answer 1

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}

Answer 2

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