$A$ guitar string of length $90\,cm$ vibrates with a fundamental frequency of $120\,Hz.$ The length of the string producing a fundamental frequency of $180\,Hz$ will be $...........cm$.

$A$ string of length $2 \ m$ is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of $500 \ Hz$,then the waves would travel on it with a velocity of ..... $m/s$.

$A$ stretched wire of length $260 \ cm$ is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2:3:4$. Their lengths must be

$A$ sonometer wire under suitable tension having specific gravity $\varrho$,vibrates with frequency $n$ in air. If the load is completely immersed in water,the frequency of vibration of the wire will become:

$A$ string is divided into three segments such that the segments possess fundamental frequencies in the ratio $1: 2: 3$. Then,the lengths of the segments are in the ratio:

If the fundamental frequency of a string is $220 \, cps$,the frequency of the fifth harmonic will be ......... $cps$.