Two uniform strings A and B made of steel are | vedclass

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

Question

(B) The fundamental frequency of a stretched string is given by $n = \frac{1}{2l} \sqrt{\frac{T}{m}}$,where $m = \pi r^2 \rho$ is the mass per unit le

Vedclass · Accepted Answer

$1: 3$

Vedclass · Answer

(B) The fundamental frequency of a stretched string is given by $n = \frac{1}{2l} \sqrt{\frac{T}{m}}$,where $m = \pi r^2 \rho$ is the mass per unit length.Thus,$n = \frac{1}{2lr} \sqrt{\frac{T}{\pi \rho}}$.The frequency of the $p$-th overtone is $(p+1)n$.For string $A$,the first overtone is $2n_A = \frac{2}{2l_A r_A} \sqrt{\frac{T}{\pi \rho}} = \frac{1}{l_A r_A} \sqrt{\frac{T}{\pi \rho}}$.For string $B$,the second overtone is $3n_B = \frac{3}{2l_B r_B} \sqrt{\frac{T}{\pi \rho}}$.Given $2n_A = 3n_B$ and $r_A = 2r_B$:$\frac{1}{l_A r_A} = \frac{3}{2l_B r_B}$$\frac{l_A}{l_B} = \frac{2 r_B}{3 r_A} = \frac{2 r_B}{3(2 r_B)} = \frac{2}{6} = \frac{1}{3}$.Therefore,the ratio of the lengths $l_A : l_B = 1 : 3$.

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$,the ratio of the lengths of the strings is :

Similar Questions

The hand of a man,the wing of a bat,and the flipper of a seal represent:

The work functions for metals $A, B$ and $C$ are respectively $1.92\, eV, 2.0\, eV$ and $5\, eV$. According to Einstein's photoelectric equation,which of these metals will emit photoelectrons for an incident radiation of wavelength $4100\, \mathring{A}$?

The molar heat capacity of water at constant pressure is $75 \ J \ K^{-1} \ mol^{-1}$. When $1 \ kJ$ of heat is supplied to $100 \ g$ of water,which is free to expand,the increase in temperature of water is ............... $K$.

Leaves that produce microspores and megaspores are called:

The radius of the circle $r = \sqrt{3} \sin \theta + \cos \theta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module