$A$ stretched string of $1 \ m$ length and mass $5 \times 10^{-4} \ kg$ is having a tension of $20 \ N$. If it is plucked at $25 \ cm$ from one end,then it will vibrate with a frequency of ... $Hz$.

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

Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water,the length of the loops changes by a factor of $2.2$. The specific gravity of the material of the cylinder is

$A$ string is stretched between fixed points separated by $75.0\, cm$. It is observed to have resonant frequencies of $420\, Hz$ and $315\, Hz$. There are no other resonant frequencies between these two. Then,the lowest resonant frequency for this string is .... $Hz$

$A$ string is clamped at both ends and it is vibrating in its $4^{th}$ harmonic. The equation of the stationary wave is $Y = 0.3 \sin(0.157 x) \cos(200\pi t)$. The length of the string is ..... $m$ (all quantities are in $SI$ units).

$A$ violin emits sound waves of frequency $n_1$ under tension $T$. When tension is increased by $44\%$,keeping the length and mass per unit length constant,the frequency of sound waves becomes $n_2$. The ratio of frequency $n_2$ to frequency $n_1$ is: