A uniform wire of length L and mass M is stretched between two fixed points, keeping a tension F. A sound of frequency μ is impressed on it. Then the maximum vibrational energy is existing in the wire when μ=

Question

A uniform wire of length L and mass M is stretched between two fixed points, keeping a tension F. A sound of frequency μ is impressed on it. Then the maximum vibrational energy is existing in the wire when μ= (A) (1/2) √( ML / F ) (B) √( FL / M ) (C) 2 × √( FM / L ) (D) (1/2) √( F / ML )

Tardigrade Admin · Accepted Answer

m propto(F)a(M)b(L)c T -1=( MLT -2) a ( M ) b ( L ) c T-1=Ma+b La+c T-2 a a+b=0 b=(-1/2) a+c=0 c=(-1/2) -2 a=-1 a=(1/2) μ=k F1 / 2 M-1 / 2 L-1 / 2 μ=k √(F/M L)

Q. A uniform wire of length $L$ and mass $M$ is stretched between two fixed points, keeping a tension $F . A$ sound of frequency $μ$ is impressed on it. Then the maximum vibrational energy is existing in the wire when $μ =$

$\frac{1}{2} \frac{M L}{F}$

$\frac{F L}{M}$

$2 \times \frac{FM}{L}$

$\frac{1}{2} \frac{F}{M L}$

$m \propto (F)^{a} (M)^{b} (L)^{c}$
$T^{- 1} = (M L T^{- 2})^{a} (M)^{b} (L)^{c}$
$T^{- 1} = M^{a + b} L^{a + c} T^{- 2 a}$
$a + b = 0 b = \frac{- 1}{2}$
$a + c = 0 c = \frac{- 1}{2}$
$- 2 a = - 1 a = \frac{1}{2}$
$μ = k F^{1/2} M^{- 1/2} L^{- 1/2}$
$μ = k \frac{F}{M L}$

Q. A uniform wire of length L and mass M is stretched between two fixed points, keeping a tension F.A sound of frequency μ is impressed on it. Then the maximum vibrational energy is existing in the wire when μ=

21​FML​​

MFL​​

2×LFM​​

21​MLF​​