If we add $3 \ kg$ load to the hanger of a sonometer,the fundamental frequency becomes two times its initial value. The initial load must be (in $kg$)

$A$ string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is

When a string is divided into three segments of length $l_1, l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1, v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is

In an experiment with a sonometer,when a mass of $180\,g$ is attached to the string,it vibrates with a fundamental frequency of $30\,Hz$. When a mass $m$ is attached,the string vibrates with a fundamental frequency of $50\,Hz$. The value of $m$ is $.........\,g$.

$A$ tuning fork and a sonometer wire are sounded together and produce $4$ beats per second. When the length of the sonometer wire is $95 \ cm$ or $100 \ cm$,the frequency of the tuning fork is ..... $Hz$.

$A$ steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire up and down. $A$ standing wave with three antinodes is created when the spring is stretched by $4.0\, cm$. What stretch of the spring produces a standing wave with two antinodes with the same frequency (in $, cm$)?