A wire of length L, diameter d, and density o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The fundamental frequency of a stretched wire is given by the formula: $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $\mu$ is the linear mass den

Vedclass · Accepted Answer

$1 : 6$

Vedclass · Answer

(C) The fundamental frequency of a stretched wire is given by the formula: $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $\mu$ is the linear mass density.Linear mass density $\mu = 	ext{Area} 	imes 	ext{Density} = (\pi r^2) ho = \pi (d/2)^2 ho = \frac{\pi d^2 ho}{4}$.Substituting $\mu$ into the frequency formula: $n = \frac{1}{2L} \sqrt{\frac{T}{\frac{\pi d^2 ho}{4}}} = \frac{1}{Ld} \sqrt{\frac{T}{\pi ho}}$.For the first wire: $n_A = \frac{1}{Ld} \sqrt{\frac{T}{\pi ho}}$.For the second wire: $n_B = \frac{1}{(2L)(3d)} \sqrt{\frac{2T}{\pi (2ho)}} = \frac{1}{6Ld} \sqrt{\frac{T}{\pi ho}}$.Taking the ratio $n_B : n_A = \frac{\frac{1}{6Ld} \sqrt{\frac{T}{\pi ho}}}{\frac{1}{Ld} \sqrt{\frac{T}{\pi ho}}} = \frac{1}{6}$.Thus, the ratio $n_B : n_A$ is $1 : 6$.

Similar Questions

Two uniform stretched steel strings $A$ and $B$ are vibrating under the same tension. The first overtone of $A$ is equal to the second overtone of $B$. If the radius of $A$ is twice that of $B$,then the ratio of the lengths of the strings $l_A/l_B$ is:

$A$ stretched string of $1 \ m$ length and mass $5 \times 10^{-4} \ kg$ is having a tension of $20 \ N$. If it is plucked at $25 \ cm$ from one end,then it will vibrate with a frequency of ... $Hz$.

$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched under a tension $T$. The correct relation between its fundamental frequency $f$,the length $L$,and the diameter $D$ is:

$A$ wire of length $1 \,m$ under a certain initial tension emits a sound of fundamental frequency $256 \,Hz$. When the tension is increased by $1 \,kg \,wt$,the frequency of the fundamental note increases to $320 \,Hz$. The initial tension is ........... $kg \,wt$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module