A 0.90 m segment of nylon cord (density 1.15 × 10³ kg/m³) is stretched between two supports that are 0.75 m apart. The surplus length is wrapped around the support on the left. A lightweight mechanical driver attached at the left support oscillates vertically at a fixed frequency of 40 Hz, producing a standing wave with four antinodes between the supports.
(a) Determine the wavelength of the standing wave formed on the cord.
(b) Using geometric considerations, calculate the actual linear mass density of the vibrating portion of the cord if its diameter is 2.0 mm.
(c) From your results in parts (a) and (b) and the given frequency, calculate the tension in the cord required to maintain the observed standing wave pattern.
(d) The driver amplitude is doubled while all other conditions remain fixed. Predict qualitatively how the tension, wavelength, and frequency of the standing wave will change, if at all, and justify each prediction.