In: Physics
$$ \begin{array}{l} \begin{array}{l} \text { Amplitude }(A)=0.2 \mathrm{~mm} \\ =2 \times 10^{-4} \mathrm{~m} \end{array} \\ \text { Frequency }(f)=530 \mathrm{~Hz} \\ \text { Speed }(v)=196 \mathrm{~m} / \mathrm{s} \end{array} $$
Angular Frequency \(\omega=2 \pi f\)
$$ \begin{array}{l} =2 \pi(530 \mathrm{~Hz}) \\ =3330 \mathrm{rad} / \mathrm{s} \end{array} $$
Angular wave number \(k=\frac{\omega}{v}\)
$$ \begin{array}{l} =\left(\frac{3330 \mathrm{rad} / \mathrm{s}}{196 \mathrm{~m} / \mathrm{s}}\right) \\ =16.9 \mathrm{rad} \mathrm{m} \end{array} $$
(b) \(\quad\) Mass per unit leng th of the wire \((\mu)=3.5 \mathrm{~g} / \mathrm{m}\)
$$ =3.5 \times 10^{-3} \mathrm{~kg} / \mathrm{m} $$
Tension in the string \(T=v^{2} \mu\)
$$ \begin{array}{l} =(196 \mathrm{~m} / \mathrm{s})^{2}\left(3.5 \times 10^{-3} \mathrm{~kg} / \mathrm{m}\right) \\ =134.4 \mathrm{~N} \end{array} $$