Question

9. The ratio of frequencies of two wires having same
length and same tension and made of the same
material is 2 : 3. If the diameter of one wire be
0.09 cm, then determine the diameter of the other.
(Ans. 0.06 cm)​

Answer 1

The diameter of the other wire is 0.06 cm.

Explanation:

Given data:

Ratio of frequencies = 2:3

Diameter of one wire = 0.09 cm

Diameter of other wire = ?

Solution:

f = 1/2L √T / μ

Ratio of frequencies "f1 / f2" = 2/3 = √ μ2 / μ1

[Since μ2 / μ1 = 4/ 9]

Now the density will also be same

so ρ = M/ V = M / L.A

ρ = μ / a =>  μ = ρA   (A = area of cross section)

Now

v = μ2 / μ1 = A2 / A1  [ A = π/4 d^2]

4 /9 = d^2 / 0.09

d = √ 4/9 x (0.09)^2

d = 6/100 = 0.06 cm

Thus the diameter of the other wire is 0.06 cm.

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