The transverse displacement in a streched string is given by
$y = 0.06 \sin \, \left( {\frac{{2\pi }}{3}x} \right)\cos \,(120\pi t)$

where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5\, m$ and  its mass is $3.0 \times 10^{-2} \,kg$, then tension in string is ..... $N$

A stretched string of $1m$ length and mass $5 \times {10^{ - 4}}kg$ is having tension of $20N.$ If it is plucked at $25cm$ from one end then it will vibrate with frequency ... $Hz$

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

In Melde's experiment, the string vibrates in $4$ loops when a $50 \,gram$ weight is placed in the pan of weight $15\, gram.$ To make the string to vibrates in $6$ loops the weight that has to be removed from the pan is

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

Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is $1 : 4 : 9 : 16$ then the ratio of their fundamental frequencies are