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Two wires made up of the same material are of equal lengths but their diameters are in the ratio 1: 2. on stretching each of these two strings by the same tension, the ratio between the fundamental frequencies of these strings is (a) 1: 4 (b) 1: 2 (c) 2: 1 (d) 4: 1

Two wires made up of the same material are of equal lengths but their diameters are in the ratio 1: 2. on stretching each of these two strings by the same tension, the ratio between the fundamental frequencies of these strings is
(a) 1: 4
(b) 1: 2
(c) 2: 1
(d) 4: 1

Grade:Upto college level

2 Answers

Arun
25763 Points
one year ago
material is same ∴ ρ1 = ρ2 length is same ∴ L1 = L2  radi r1 : r2 = 1:2 Tension is same ∴ T1 = T2 as L, T, ρ are same f ∝ (1/√r2) = (1/r) ∴ (f1/f2) = (r2/r1) = (2/1)
Vikas TU
14149 Points
one year ago
Dear student 
v = sqrt(T/mew) 
mew = pi*r^2 *rho 
where r is the radius or the string and ρ is the density of the material of the string.
v = 1/r sqrt(T/pi*rho)
v ∝ 1/r 
va/vb = rb/ra = 1/2 

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