A tuning fork resonates with a sonometer wire | vedclass

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

Question

(C) The frequency of a sonometer wire is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is length,$T$ is tension,and $\mu$ is linear mass

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) The frequency of a sonometer wire is given by $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $L$ is length,$T$ is tension,and $\mu$ is linear mass density.Since $L$ and $\mu$ are constant,$f \propto \sqrt{T}$.Let $f_0$ be the frequency of the tuning fork.For $T_1 = 6 \ N$,the wire resonates with the tuning fork,so $f_1 = f_0 = k\sqrt{6}$,where $k = \frac{1}{2L\sqrt{\mu}}$.For $T_2 = 54 \ N$,the frequency of the wire is $f_2 = k\sqrt{54} = k\sqrt{9 	imes 6} = 3k\sqrt{6} = 3f_0$.The number of beats per second is $|f_2 - f_0| = 12$.Substituting $f_2 = 3f_0$,we get $|3f_0 - f_0| = 12$.$2f_0 = 12$,which gives $f_0 = 6 \ Hz$.

$A$ tuning fork resonates with a sonometer wire of length $1 \ m$ stretched with a tension of $6 \ N$. When the tension in the wire is changed to $54 \ N$,the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is $Hz$.

Similar Questions

$A$ certain string will resonate at several frequencies,the lowest of which is $200 \,Hz$. What are the next three higher frequencies at which it resonates?

$A$ tuning fork is sounded with a sonometer wire of length $95 \, cm$ or $100 \, cm$,producing $4$ beats per second in both cases. What is the frequency of the tuning fork in $Hz$?

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

When the tension in a string is increased by $3 \ kg \ wt$,the frequency of the fundamental mode increases in the ratio $2:3$. The initial tension in the string is: (in $kg \ wt$)

The fundamental frequency of a sonometer wire is $50 \text{ Hz}$ for a given length and tension. If the length is increased by $25 \%$ while keeping the tension constant,what is the percentage change in the frequency of the second harmonic?

Vedclass Test Series

Exam Paper Generator

Online Exam Module