A sonometer wire is in unison with a tuning f | vedclass

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

Question

(D) The frequency of vibration $v$ of a sonometer wire is given by the formula:$v = \frac{1}{2L} \sqrt{\frac{T}{m}}$where $T$ is the tension (weight $

Vedclass · Accepted Answer

$2:1$

Vedclass · Answer

(D) The frequency of vibration $v$ of a sonometer wire is given by the formula:$v = \frac{1}{2L} \sqrt{\frac{T}{m}}$where $T$ is the tension (weight $w$) and $m$ is the mass per unit length.For the first case,the frequency is:$v = \frac{1}{2L_1} \sqrt{\frac{w}{m}} \quad (i)$For the second case,the weight is reduced to $\frac{w}{4}$ and the length becomes $L_2$:$v = \frac{1}{2L_2} \sqrt{\frac{w/4}{m}} = \frac{1}{2L_2} \cdot \frac{1}{2} \sqrt{\frac{w}{m}} = \frac{1}{4L_2} \sqrt{\frac{w}{m}} \quad (ii)$Since the tuning fork frequency $v$ remains constant,we equate $(i)$ and $(ii)$:$\frac{1}{2L_1} \sqrt{\frac{w}{m}} = \frac{1}{4L_2} \sqrt{\frac{w}{m}}$$\frac{1}{2L_1} = \frac{1}{4L_2}$$4L_2 = 2L_1$$\frac{L_1}{L_2} = \frac{4}{2} = 2$Therefore,the ratio $\frac{L_1}{L_2}$ is $2:1$.

$A$ sonometer wire is in unison with a tuning fork when it is stretched by weight $w$ and the corresponding resonating length is $L_1$. If the weight is reduced to $\frac{w}{4}$,the corresponding resonating length becomes $L_2$. The ratio $\frac{L_1}{L_2}$ is:

Similar Questions

$A$ stretched wire of length $260 \ cm$ is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2:3:4$. Their lengths must be

The fundamental frequency of a sonometer wire is $n$. If the tension is increased $3$ times,the length is increased $3$ times,and the diameter is increased $2$ times,what will be the new frequency?

$A$ stretched string is vibrating in the second overtone. The number of nodes and antinodes between the ends of the string are respectively:

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y =$ Young's modulus,$\rho =$ density,$\alpha =$ coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

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 length of string $B$ to that of $A$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module