$A$ 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 $n_{1}, n_{2}$ and $n_{3}$ are the fundamental frequencies of three segments into which a string is divided,then the original fundamental frequency $n$ of the string is given by

The fundamental frequency of a sonometer wire is $50 \ Hz$ 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?

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:

$A$ wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \;Hz$. The mass of the wire is $3.5 \times 10^{-2} \;kg$ and its linear mass density is $4.0 \times 10^{-2} \;kg \;m^{-1}$. What is
$(a)$ the speed of a transverse wave on the string,and
$(b)$ the tension in the string?

$A$ segment of wire vibrates with a fundamental frequency of $450 \,Hz$ under a tension of $9 \,kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 \,Hz$ is: