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 $Hz$)

To increase the frequency of a stretched string from $100 \ Hz$ to $400 \ Hz$,the tension in the string has to be changed by how many times?

$A$ sonometer wire,with a suspended mass of $M = 1 \, kg$,is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is $(1/6)$ that on earth. To obtain resonance on the moon,the value of $M$ should be ......... $kg$.

If we add $3 \ kg$ load to the hanger of a sonometer,the fundamental frequency becomes two times its initial value. The initial load must be (in $kg$)

$A$ 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 $Hz$.

Two vibrating strings $A$ and $B$ of the same material but lengths $3 L$ and $2 L$ have radii $2 r$ and $3 r$ respectively. They are stretched under the same tension. String $A$ vibrates in the second overtone and string $B$ in the fundamental mode. The ratio of their frequencies $n_A / n_B$ will be: