You have a trough \(3.60 \mathrm{~m}\) long. It is filled with water, and you want to create a standing wave such that a node occurs every \(0.30 \mathrm{~m}\).

(a) What is the wavelength of this wave?

(b) A leaf floating on the water \(0.60 \mathrm{~m}\) from one end of the trough is displaced a vertical distance \(D_{y}=10 \mathrm{~mm}\) at \(t=3.2 \mathrm{~s}\), and the leaf's displacement has a period of \(0.60 \mathrm{~s}\). What is the resultant displacement of the standing wave?

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