A plucked violin string carries a traveling wave given by the equation

\[f(x, t)=a \sin \left[b(x-c t)+\phi_{\mathrm{i}}\right],\]

with \(a=0.00580 \mathrm{~m}, b=33.05 \mathrm{~m}^{-1}\), and \(c=245 \mathrm{~m} / \mathrm{s}\).

(a) If \(f(0,0)=0\), what is \(\phi_{1}\) ?

(b) Determine the simple harmonic period of a point on the string.