$A$ tuning fork produces $5 \, Hz$ beats per second when the length of a sonometer wire is either $1 \, m$ or $1.05 \, m$. Calculate the frequency of the tuning fork in $Hz$.

$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched under a tension $T$. The correct relation between its fundamental frequency $f$,the length $L$,and the diameter $D$ is:

If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved,then its fundamental frequency will become

$A$ wire of length $L$ and linear density $m$ is stretched between two rigid supports with tension $T$. It is observed that the wire resonates in the $P^{th}$ harmonic at a frequency of $320 \ Hz$ and resonates again at the next higher frequency of $400 \ Hz$. The value of $p$ is:

The correct graph between the frequency $n$ and the square root of density $(\rho)$ of a wire,keeping its length,radius,and tension constant,is:

When a sonometer wire vibrates in the third overtone, the number of antinodes and nodes formed on the wire are respectively