Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in 2 s. The initial frequency of each wire is

Question

Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in 2 s. The initial frequency of each wire is (A) 150 Hz (B) 200 Hz (C) 300 Hz (D) 450 Hz

Tardigrade Admin · Accepted Answer

n1=k√T, n2=k√1.01 T ∵ n2-n1=(3/2) k(√1.01 T - √T)=1.5 k√T[(1 + 0.01)(1/2) - 1]=1.5 k√T[1 + (1/2) × 0.01 - 1]=1.5 k√T=(1.5 × 2/0.01) =(1.5 × 2/0.01) =300 Hz

Q. Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in $2 s .$ The initial frequency of each wire is

$150 Hz$

$200 Hz$

$300 Hz$

$450 Hz$

$n_{1} = k T, n_{2} = k 1.01 T$
$∵ n_{2} - n_{1} = \frac{3}{2}$
$k (1.01 T - T) = 1.5$
$k T [(1 + 0.01)^{\frac{1}{2}} - 1] = 1.5$
$k T [1 + \frac{1}{2} \times 0.01 - 1] = 1.5$
$k T = \frac{1.5 \times 2}{0.01}$
$= \frac{1.5 \times 2}{0.01}$
$= 300 Hz$

Q. Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in 2s. The initial frequency of each wire is

150Hz

200Hz

300Hz

450Hz