The amplitude of a wave traveling on a string is \(0.250 \mathrm{~m}\). The \(80.0-\mathrm{Hz}\) wave is traveling in the positive \(x\) direction at a wave speed of \(17.5 \mathrm{~m} / \mathrm{s}\).

(a) Determine its wavelength, and write the equation for its timeindependent wave function.

(b) For \(t=3.00 \mathrm{~s}\), compute the displacement and transverse velocity of the point on the string at \(x=1.25 \mathrm{~m}\), assuming an initial phase \(\phi_{\mathrm{i}}\) of zero.

(c) Write the time-dependent wave function for the wave.

(d) If the string displacement at \(x=1.25 \mathrm{~m}\) is \(0.210 \mathrm{~m}\) at \(t=3.00 \mathrm{~s}\), write the timedependent wave function that uses the smallest possible value of \(\phi_{\mathrm{i}}\).