The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth, its frequency will be changed to ........... $cps$

A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = young’s modulus, $\rho$ = density, $\alpha$ = coefficient of linear expansion) then the frequency of transverse vibration is proportional to : 

A second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The point where the string has to be plucked and touched are

A tuning fork gives $4$ beats with $50\, cm$ length of a sonometer wire if the length of  the wire is shortened by $1\, cm$. the no. of beats still the same. The frequency of the  fork is -............. $\mathrm{Hz}$

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

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by ..... $\%$