A wave traveling along a string is described by

\[f(x, t)=a \sin (\pi b x+q t),\]

with \(a=30 \mathrm{~mm}, b=0.33 \mathrm{~m}^{-1}\), and \(q=10.47 \mathrm{~s}^{-1}\).

(a) Calculate the amplitude, wavelength, period, and speed of the wave.

(b) Compute the \(y\) component of the displacement of the string at \(x=0.500 \mathrm{~m}\) and \(t=1.60 \mathrm{~s}\).