91Ó°ÊÓ

The length of the string isL = 125 cm or 1.25 m.

The mass of the string is M = 2.00 g or 0.002 kg .

The tension in the string is $\mathrm{Ï„}=7.00\mathrm{N}$.

By using the formulas for the wave speed and the lowest resonant frequency, we can find the wave speed and the lowest resonant frequency of the string respectively.

Formula:

The speed of the wave $v=\sqrt{\frac{\mathrm{τ}}{\mathrm{μ}}}..........\left(1\right)$

The linear density of the string,$\mathrm{μ}=\frac{M}{L}.........\left(2\right)$

The resonant frequency of the wave, $f=\frac{v}{\mathrm{λ}}.........\left(3\right)$

Using equation (2) in equation (1), we get the speed of the wave as given:

$$\begin{gathered} v=\sqrt{\frac{\mathrm{τ}L}{M}} \\ =\sqrt{\frac{7.00×1.25}{0.002}} \\ =66.1\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the speed of the wave is 66.1 m/s

But, the wavelength of the wave with lowest resonant frequency$f_1$is${\mathrm{λ}}_1=2L$, therefore, using this in the equation (3) and the given values, we get the lowest frequency as given:

$$\begin{gathered} f_1=\frac{v}{2L} \\ =\frac{66.1}{2×1.25} \\ =26.4\mathrm{Hz} \end{gathered}$$

Hence, the value of lowest frequency is 26.4 Hz