The length of the wire shown in figure between the pulleys is $1.5\, m$ and its mass is  $12.0\,g$. The frequency of vibration with which the wire vibrates in three loops forming antinode at the mid point of the wire is $(g = 9.8 \,m/s^2)$

A tuning fork of frequency $280\,\, Hz$ produces $10$ beats per sec when sounded with a vibrating sonometer string. When the tension in the string increases slightly, it produces $11$ beats per sec. The original frequency of the vibrating sonometer string is … $Hz$

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by ….. $\%$

Length of a string tied to two rigid supports is $40 cm$. Maximum length (wavelength in $cm$) of a stationary wave produced on it is … $cm$

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$…..$