$A$ sonometer wire of length $25 \,cm$ vibrates in unison with a tuning fork. When its length is decreased by $1 \,cm$, $6$ beats are heard per second. What is the frequency of the tuning fork (in $\,Hz$)?

Two strings $A$ and $B$ of lengths $L_A = 80 \text{ cm}$ and $L_B = x \text{ cm}$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency, the value of $x$ is:

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes,the one of length $L$ with frequency $n_1$ and the other with frequency $n_2$. The ratio $n_1/n_2$ is given by

The fundamental frequency of a sonometer wire is $n$. If the length,tension,and diameter of the wire are all tripled,what is the new fundamental frequency?

When a stretched wire of fundamental frequency $f$ is divided into three segments,the fundamental frequencies of these three segments are $f_1, f_2$ and $f_3$ respectively. Then the relation among $f_1, f_2, f_3$ and $f$ is (Assume tension is constant).

Length of a sonometer wire is either $95 \ cm$ or $100 \ cm$. In both the cases,a tuning fork produces $5 \ beats/sec$ with the wire. The frequency of the tuning fork is- (in $Hz$)