A wire of density $8 \times 10^3\,kg / m ^3$ is stretched between two clamps $0.5\,m$ apart. The extension developed in the wire is $3.2 \times 10^{-4}\,m$. If $Y =8 \times 10^{10}\,N / m ^2$, the fundamental frequency of vibration in the wire will be $......\,Hz$.

The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$. Consider the following statements

$I.$ The speed of the wave is $4n \times ab$

$II.$ The medium at $a$ will be in the same phase as $d$ after $\frac{4}{{3n}}s$

$III.$ The phase difference between $b$ and $e$ is $\frac{{3\pi }}{2}$

Which of these statements are correct

A pipe $20$ $\mathrm{cm}$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of $1237.5$ $\mathrm{Hz}$ ?( sound velocity in air $= 330$ $\mathrm{m/s}$ ).

What will be the change in phase of wave due to reflection from rigid support ?

A person is producing wave in string by moving his hand first up and then down. If frequency is $\frac{1}{8}\,Hz$ then find out time taken by particle which is at a distance of $9\,m$ from source to move to lower extreme first time .... $s$ . (Given $\lambda  = 24\, m$)

If vibrations of a string are to be increased by a factor of two, then tension in the string must be made