Question

Assuming that the frequency of vibrating string may be depend upon applied force, length, mass per unit

Answer 1

Answer:

Explanation:

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, ,here k is constant and if k = 1