II. Superposition and standing waves Chapter 17 If two waves are solutions of a linear wave equation, then any linear combination of the 2 waves is also a solution. A standing wave is an oscillation with space and time decoupled: (1) Its amplitude varies sinusoidally with position. (2) At all points the amplitude is proportional to cos for} and at certain times the amplitude is zero everywhere! The acceleration of gravity is 9.81 m s-2. The angular frequency of a simple pendulum of length / is /g/ / . You are given a I'm long hollow tube with open ends, and with a 0.02 m inside diameter in the ambient air. (a) What are the resonant frequencies (in Hz) of the third lowest frequency longitudinal oscillation of the air in the tube? (b) What length / of a similar tube (in m), that is closed at one end, will have the same fundamental resonance frequency as the fundamental resonance frequency of the open-ended 1 m tube of part (a)? (c) What is the lowest resonant frequency (in Hz) of a tube made by joining the open-ended tube of part (a) to the open end of the closed tube of part (b)? (d) The one meter open tube of part (a) is being continuously excited by a sinusoidal oscillating pressure at its center so that the air in the tube is oscillating at its lowest resonant frequency. At what distances, y, measured on a line perpendicular to the tube and going straight out from the center of the tube, will you detect (with a small microphone) constructive interference due to the two waves emanating from the ends of the tube