A piano string $1.5\,m$ long is made of steel of density $7.7 \times 10^3 \,kg/m^3$ and  Young’s modulus $2 \times 10^{11} \,N/m^2$. It is maintained at a tension which produces  an elastic strain of $1\%$ in the string. The fundamental frequency of transverse vibrations of string is ……… $Hz$

The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-

The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$ where $x$ and $y$ are in centimetre and $t$ in second. The separation between two adjacent nodes is …. $cm$

A string of length $1\ m$ fixed at both ends is vibrating in $3^{rd}$ overtone. Tension in string is $200\ N$ and linear mass density is $5\ gm/m$ . Frequency of these vibrations is ….. $Hz$

The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ……… $\%$