$A$ sonometer wire of length $1.5 \ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \ kg/m^3$ and $2.2 \times 10^{11} \ N/m^2$ respectively (in $Hz$)?

$A$ stretched string is divided into three segments of lengths $50\,cm$,$40\,cm$,and $10\,cm$ with the help of bridges. Their vibrations will have frequencies in the ratio:

If the length of a stretched string is shortened by $40\%$ and the tension is increased by $44\%$,then the ratio of the final and initial fundamental frequencies is

In an experiment to study standing waves,you use a string whose mass per unit length is $\mu = (1.0 \pm 0.1) \times 10^{-4} \ kg/m$. You look at the fundamental mode,whose frequency $f$ is related to the length $L$ and tension $T$ of the string by the equation $L = \frac{1}{2f} \sqrt{\frac{T}{\mu}}$. You make a plot with $L$ on the $y$-axis and $\sqrt{T}$ on the $x$-axis,and find that the best-fitting line is $y = (8.0 \pm 0.3) \times 10^{-3}x + (0.2 \pm 0.04)$ in $SI$ units. What is the value of the frequency of the wave (including the error)? Express your result in $SI$ units $(Hz)$.

The fundamental frequency of a sonometer with a weight of $4\,kg$ is $256\,Hz$. The weight required to produce its octave is .... $kg-wt$

$A$ sonometer wire of resonating length $90 \ cm$ has a fundamental frequency of $400 \ Hz$ when kept under some tension. The resonating length of the wire with a fundamental frequency of $600 \ Hz$ under the same tension is . . . . . . $cm$.