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 4kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.7 rad/s and an amplitude of 260cm. 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? (c) If the mass of the block is doubled instead, what happens to the distance between adjacent nodes?

Question

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 4kg block hanging from the other end of the rope over a pulley. The oscillator has an angular frequency of 44.7 rad/s and an amplitude of 260cm.  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? (c) If the mass of the block is doubled instead, what happens to the distance between adjacent nodes?

Damon · Answer

T = 4 * 9.81 = 39.24 Newtons tension
c = velocity of wave = sqrt(T/mu) = sqrt (39.24 * 10^2 /5.4) = 10 sqrt(39.24/5.4)
= 27 meters/second
omega = 2 pi f = 44.7
so f = 7.11 hz and T = 1/f = 0.14 second
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html
what is wavelength?
distance = speed * time
lambda = c T = 27 * 0.14 = 3.8 meter wavelength
half a wavelength between nodes = 1.9 meters between nodes
That should get you started.