A uniform metal wire of density $\rho $, cross-sectional area $A$ and length $L$ is stretched with a tension $T$. The speed of transverse wave in the wire is given by

A vibrating string of certain length $l$ under a tension $T$ reasonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75$ $cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340$ $m/s$, the frequency $n$ of the tuning fork in $Hz $ is

A device used for investigating the vibration of a fixed string or wire is

A sine wave of wavelength $\lambda $ is travelling in a medium. The minimum distance between the two particles, always having same speed, is

The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ......... $\%$

A clamped string is oscillating in $n^{th}$ harmonic, then