If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved,then its fundamental frequency will become

Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water,the length of the loops changes by a factor of $2.2$. The specific gravity of the material of the cylinder is

The given diagram shows three light pieces of paper placed on a wire that is stretched over two supports,$Q$ and $R$,a distance $4x$ apart. When the wire is made to vibrate at a particular frequency,all the pieces of paper,except the middle one,fall off the wire. Which of the following could be the wavelength of the vibration (in $x$)?

The length of the wire shown in the figure between the pulleys is $1.5 \, m$ and its mass is $12.0 \, g$. The frequency of vibration with which the wire vibrates in three loops,forming an antinode at the midpoint of the wire,is: (Given $g = 9.8 \, m/s^2$)

$A$ string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is .... $Hz$

The fundamental frequency of a sonometer wire of length $l$ is $n_0$. $A$ bridge is now introduced at a distance of $\Delta l$ (where $\Delta l \ll l$) from the center of the wire. The lengths of wire on the two sides of the bridge are now vibrated in their fundamental modes. Then,the beat frequency is nearly