1: Green Sarge is once again trapped behind Beige army's lines. He reaches an impassible ravine and is forced to look for a crossing. A mile upstream, Sarge finds that the Beige army has set up a pair of taut metal wires that span the perilous ravine. Each wire is 2 cm in diameter, and is made out of steel, with density 7 g/cm3. The gap is 20m across, and at center span the wire hangs 1 m below the level of the ground on either side.
Sarge quickly approximates the rope to be a string with a very high spring constant. He estimates that the unstretched length of rope is exactly 20m, and that the additional stretch is due to half the mass of the rope being applied as a downward force in the middle of the span.
A: What is the speed of wave propagation on the rope?
Sarge notices that the cable is susceptible to vibrations. He drives the rope at a frequency such that the center of the span goes through the largest amount of motion.
B: What frequency does Sarge drive the rope at?
C: What are the wavelength and frequency of the sound wave that is created (speed of sound in air = 340 m/s)?