$A$ string vibrates with a frequency of $200 \ Hz$. When its length is doubled and tension is altered,it begins to vibrate with a frequency of $300 \ Hz$. The ratio of the new tension to the original tension is

The length of the string of a musical instrument is $90 \;cm$ and has a fundamental frequency of $120 \;Hz$. Where (in $cm$) should it be pressed to produce a fundamental frequency of $180 \;Hz$?

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

$A$ thin wire of length $99 \ cm$ is fixed at both ends as shown in the figure. The wire is kept under a tension and is divided into three segments of lengths $l_1, l_2$ and $l_3$ as shown in the figure. When the wire is made to vibrate, the segments vibrate respectively with their fundamental frequencies in the ratio $1: 2: 3$. Then, the lengths $l_1, l_2$ and $l_3$ of the segments respectively are (in $cm$):

The correct graph between the frequency $n$ and the square root of density $(\rho)$ of a wire,keeping its length,radius,and tension constant,is:

The frequency of a sonometer wire is $100 \ Hz$. When the weights producing the tension are completely immersed in water,the frequency becomes $80 \ Hz$,and on immersing the weights in a certain liquid,the frequency becomes $60 \ Hz$. The specific gravity of the liquid is: