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

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 ….. $N$

When an air column at $15\,^oC$ and a tunning fork are sounded together then $4$ beats per second are produced, the frequency of the fork is less then that of air column. When the temperature falls to $10\,^oC$ , then the beat frequency decreases by one. The frequency of the fork will be ….. $Hz$ $[V_{sound}$ at $0\,^oC = 332\,m/s]$

Fundamental frequency of one closed pipe is $300$ $\mathrm{Hz}$. What will be the frequency of its second overtone ?

A wire of density $8 \times 10^3\,kg / m ^3$ is stretched between two clamps $0.5\,m$ apart. The extension developed in the wire is $3.2 \times 10^{-4}\,m$. If $Y =8 \times 10^{10}\,N / m ^2$, the fundamental frequency of vibration in the wire will be $……\,Hz$.