The fundamental frequency of a sonometer 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

In a sonometer wire, the tension is maintained by suspending a $50.7 kg$ mass from the free end of the wire. The suspended mass has a volume of $ 0.0075 \, m^3$. The fundamental frequency of the wire is $260 Hz$. If the suspended mass is completely submerged in water, the fundamental frequency will become …. $Hz$ (take $g = 10 ms^{-2}$)

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 ………… $Hz$

The equation of a wave on a string oflinear mass density $0.04$ $kgm^{-1}$ is given by

$y = 0.02sin\left[ {2\pi \left( {\frac{t}{{0.04\left( s \right)}} – \frac{x}{{0.50\left( m \right)}}} \right)} \right]m$ The tension in the string is  …. $N$