$A$ $1 \, cm$ long string vibrates with a 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: (in $, Hz$)

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

$A$ string of length $100 \,cm$ has three resonant frequencies, $120 \,Hz, 200 \,Hz$ and $280 \,Hz$. If a node is formed at the end of the string, the speed of the transverse wave on this string is : (in $\,m/s$)

At poles,a stretched wire of a given length vibrates in unison with a tuning fork. At the equator,for the same setting,to produce resonance with the same fork,the vibrating length of the wire

$A$ sonometer wire '$A$' of diameter '$d$' under tension '$T$' having density '$\rho_1$' vibrates with fundamental frequency '$n$'. If we use another wire '$B$' which vibrates with the same frequency under tension '$2T$' and diameter '$2d$',then the density '$\rho_2$' of wire '$B$' will be:

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: (in $Hz$)