As in the figure below, a simple harmonic oscillator is attached to a rope of linear mass density 5.4 ✕ 10^−2 kg/m, creating a standing transverse wave. There is a 3.2-kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.3 rad/s and an amplitude of 256.0 cm.
(a) What is the distance between adjacent nodes?
(b) If the angular frequency of the oscillator doubles, what happens to the distance between adjacent nodes? (Enter the new distance.)
(c) If the mass of the block is doubled instead, what happens to the distance between adjacent nodes? (Enter the new distance.)
(d) If the amplitude of the oscillator is doubled, what happens to the distance between adjacent nodes? (Enter the change in distance.)