When tension $T$ is applied to a sonometer wire of length $l$, it vibrates with the fundamental frequency $n$. Keeping the setup same, when the tension is increased by $8 \,N$, the fundamental frequency becomes three times the earlier. The initial tension applied to the wire was: (in $\,N$)

In an experiment with a sonometer,a tuning fork of frequency $256 \ Hz$ resonates with a length of $25 \ cm$ and another tuning fork resonates with a length of $16 \ cm$. If the tension of the string remains constant,the frequency of the second tuning fork is .... $Hz$

The length and diameter of a metal wire used in a sonometer are both doubled. The fundamental frequency will change from $n$ to:

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 $x$)?

An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water, the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$).

The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?