A string initially hanging vertically is displaced to the right with a speed of \(25 \mathrm{~m} / \mathrm{s}\) for \(0.040 \mathrm{~s}\), then returned to its original position in \(0.010 \mathrm{~s}\). This motion is repeated, with no delays, numerous times. The wave created by this motion travels down the string at \(67 \mathrm{~m} / \mathrm{s}\) and has a period of \(0.050 \mathrm{~s}\).

(a) Write the timedependent wave function for this pulse, and 

\((b)\) show that this function is a solution to the wave equation (Eq. 16. 51).

Data from Eq. 16. 51

af dx ax 2 1 a Zat