The length of a sonometer wire is $0.75\, m$ and density $9 \times 10^3\, kg/m^3$. It can bear a stress of $8.1 \times 10^8\, N/m^2$ without exceeding the elastic limit. What is the fundamental frequency that can be produced in the wire  …. $Hz$ ?

A tuning fork of frequency $340\, Hz$ is sounded above an organ pipe of length $120\, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is …. $cm$ (speed of sound in air $= 340 \,m/s$)

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 of a string clamped at its both ends is given by 

$y\left( {x,t} \right) = 2\,\sin \,\left( {\frac{{2\pi }}{3}x} \right)\,\cos \,\left( {100\,\pi t} \right)$ 

where $x$ and $y$ are in $cm$ and $t$ is in $s$. Which of the following statements is correct ?

A stretched string is vibrating in its $5^{th}$ harmonic as shown. Consider a particle $1(figure)$. At an instant this particle is at mean positions and is moving towards its negative extreme. Which of the following set of particles, are in same phase with particle $1$