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 $12 \,m$ long vibrating string has the speed of wave $48 \,m / s$. To what frequency it will resonate ……….. $cps$

The fundamental frequency of a string stretched with a weight of $4 kg$ is $256 Hz$. The weight required to produce its octave is …. $kg \,wt$

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 ….. $N$

Two wires are fixed in a sonometer. Their tensions are in the ratio $8 : 1$. The lengths are in the ratio $36:35.$ The diameters are in the ratio $4 : 1$. Densities of the materials are in the ratio $1 : 2$. If the lower frequency in the setting is $360 Hz.$ the beat frequency when the two wires are sounded together is