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 string wave equation is given $y=0.002 \sin (300 t-15 x)$ and mass density is $\mu=\frac{0.1\, kg }{m}$. Then find the tension in the string, (in $N$)

A tuning fork of frequency $280\,\, Hz$ produces $10$ beats per sec when sounded with a vibrating sonometer string. When the tension in the string increases slightly, it produces $11$ beats per sec. The original frequency of the vibrating sonometer string is … $Hz$

Stationary waves are produced in $10\,m$  long stretched string. If the string Vibrates in $5$ segments and wave velocity  $20\,m/s$ the frequency is ….. $Hz$

A tuning fork vibrating with a sonometer having a wire of length $20 \,cm$ produces $5$ beats per second. The beats frequency does not change if the length of the wire is changed to $21 \,cm$. The frequency of the tuning fork must be ………… $Hz$