Pipe C is a straight tube 0.70m in length that is closed at one end and open at the other. Pipe D is open at both ends and has an adjustable length. Both pipes are sounded simultaneously in their fundamental modes in still air where the speed of sound is 340ms−1. Beats are heard at a frequency of 4Hz.
(1) Part 1: (a) Calculate the fundamental frequency produced by pipe C. Show your work clearly.
(2) Part 2: (b) Determine the two possible lengths of pipe D that would result in the observed beat frequency. Provide numerical answers to three significant figures and explain the reasoning that leads to two possible solutions.
(3) Part 3: (c) Suppose the two pipes are now excited so that pipe C vibrates in its next higher resonant mode and pipe D vibrates in its second harmonic. For each of the two lengths found in part (b), calculate the new beat frequency that would be heard. Show all steps and comment on whether the beat frequency increases, decreases, or remains the same in each case.