Two similar sonometer wires have fundamental frequencies of $500 \, Hz$. They are under the same tension. By what percentage should the tension be increased in one wire so that the two wires produce $5 \, \text{beats/sec}$ (in $\%$)?

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

$A$ 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 given diagram shows three light pieces of paper placed on a wire that is stretched over two supports,$Q$ and $R$,a distance $4x$ apart. When the wire is made to vibrate at a particular frequency,all the pieces of paper,except the middle one,fall off the wire. Which of the following could be the wavelength of the vibration (in $x$)?

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \,cm$ or $100 \,cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $\,Hz$)

$A$ stretched string is divided into three segments of lengths $50\,cm$,$40\,cm$,and $10\,cm$ with the help of bridges. Their vibrations will have frequencies in the ratio: