Two sinusoidal waves travel along the same string. Their time-dependent wave functions are

\[\begin{aligned}
& f_{1}(x, t)=a \sin \left(b x-q t-\frac{1}{4} \pi\right) \\
& f_{2}(x, t)=a \sin \left(b x-q t-\frac{1}{3} \pi\right)
\end{aligned}\]

with \(a=5.00 \times 10^{-2} \mathrm{~m}, \quad b=0.120 \mathrm{~m}^{-1}\), and \(q=\) \(180 \mathrm{~s}^{-1}\).

(a) What is the phase difference between these two waves? 

\((b)\) Write the time-dependent wave function for the wave created by the superposition of these two waves.

(c) What is the displacement of the string at \(x=2.00 \mathrm{~m}\) at \(t=1.70 \mathrm{~s}\) ?