Four wires of identical length, diameters and of the same material are stretched on a sonometre wire. If the ratio of their tensions is $1 : 4 : 9 : 16$ then the ratio of their fundamental frequencies are

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

A $1 cm$ long string vibrates with fundamental frequency of $256\, Hz$. If the length is reduced to $\frac{1}{4}cm$ keeping the tension unaltered, the new fundamental frequency will be

A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire ?

The frequency of a sonometer wire is $f$, but when the weights producing the tensions are completely immersed in water the frequency becomes $f/2$ and on immersing the weights in a certain liquid the frequency becomes $f/3$. The specific gravity of the liquid is: 

A tuning fork vibrating with a sonometer having a wire of length $20 \,cm$ produces $5$ beats per second. The beats frequency does not change if the length of the wire is changed to $21 \,cm$. The frequency of the tuning fork must be ............ $Hz$