$\begin{aligned} & L=8 \mathrm{~m} \quad \theta_0=\cos ^{-1}(0.9) f_0=660 \mathrm{~Hz} \\ & V_s=330 \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\end{aligned}$

$\begin{aligned} & v=\sqrt{2 g l(1-\cos \theta)} \\ & =\sqrt{2 \times 10 \times 8 \times 0.1}=4 \mathrm{~m} / \mathrm{s} \\ & f_{\max }=f_0\left(\frac{v_s+v}{v_s-v}\right) \\ & f_{\min }=f_0\left(\frac{v_s-v}{v_s+v}\right) \\ & f_{\max }-f_{\min }=f_0\left(\frac{v_s+v}{v_s-v}-\frac{v_s-v}{v_s+v}\right) \\ & =f_0\left(\frac{4 \times v_s \times v}{\left(v_s^2-v^2\right)}\right)=\frac{660 \times 4 \times 330 \times 4}{\left(330^2-4^2\right)} \approx 32 \mathrm{~Hz} \\ & \Delta f=32 \mathrm{~Hz}\end{aligned}$