Question

Assuming that frequency of vibrating string depends upon the load f applied length of the string l and mass per unit length find the relation ?

Answer 1

Frequency of vibrating string depends upon
1. Load , F
2. length of string , l
3. Mass per unit length , μ

dimension of frequency , v = [T⁻¹]
dimension of load , F = [MLT⁻²]
dimension of length , l = [L]
dimension of mass per unit length , μ = [ML⁻¹]

Let relation between v,F, l and μ is in such a way ,
v = kF^al^bμ^c
Here , k is constant .
∴ [T⁻¹ ] = k [MLT⁻²]^a [L]^b[ML⁻¹]^c
[T⁻¹] = [M]^(a +c) [L]^(a +b - c) [T]^(-2a)
Compare both sides,
(a + c) = 0,
(a + b - c) = 0
-2a = -1 ⇒ a = 1/2
∴ c = a = -1/2
∴ b = c - a = -1/2 - 1/2 = -1

Hence, $\bold{v=kl\sqrt{\frac{F}{\mu}}}$,here k is constant and if k = 1
$\bold{v=l\sqrt{\frac{F}{\mu}}}$

Answer 2

Answer:

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