A 1.005 m chain consists of small spherical beads, eachwith a mass of 1.00 g and a diameter of 5.00 mm, threaded on an elasticstrand with negligible mass such that adjacent beads are separated bya center-to-center distance of 10.0 mm. There are beads at each end ofthe chain. The strand has a spring constant of 28.8 N/m. The chain isstretched horizontally on a frictionless tabletop to a length of 1.50 m,and the beads at both ends are fixed in place. (a) What is the linear massdensity of the chain? (b) What is the tension in the chain? (c) With whatspeed would a pulse travel down the chain? (d) The chain is set vibratingand exhibits a standing-wave pattern with four antinodes. What isthe frequency of this motion? (e) If the beads are numbered sequentiallyfrom 1 to 101, what are the numbers of the five beads that remain motionless?(f) The 13th bead has a maximum speed of 7.54 m/s. Whatis the amplitude of that bead’s motion? (g) If x0 = 0 corresponds to thecenter of the 1st bead and x101 = 1.50 m corresponds to the center ofthe 101st bead, what is the position xn of the nth bead? (h) What is themaximum speed of the 30th bead?

A 1.005 m chain consists of small spherical beads, eachwith a mass of 1.00 g and a diameter of 5.00 mm, threaded on an elasticstrand with negligible mass such that adjacent beads are separated bya center-to-center distance of 10.0 mm. There are beads at each end ofthe chain. The strand has a spring constant of 28.8 N/m. The chain isstretched horizontally on a frictionless tabletop to a length of 1.50 m,and the beads at both ends are fixed in place. (a) What is the linear massdensity of the chain? (b) What is the tension in the chain? (c) With whatspeed would a pulse travel down the chain? (d) The chain is set vibratingand exhibits a standing-wave pattern with four antinodes. What isthe frequency of this motion? (e) If the beads are numbered sequentiallyfrom 1 to 101, what are the numbers of the five beads that remain motionless?(f) The 13th bead has a maximum speed of 7.54 m/s. Whatis the amplitude of that bead’s motion? (g) If x0 = 0 corresponds to thecenter of the 1st bead and x101 = 1.50 m corresponds to the center ofthe 101st bead, what is the position xn of the nth bead? (h) What is themaximum speed of the 30th bead?

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Question

A 1.005 m chain consists of small spherical beads, each
with a mass of 1.00 g and a diameter of 5.00 mm, threaded on an elastic
strand with negligible mass such that adjacent beads are separated by
a center-to-center distance of 10.0 mm. There are beads at each end of
the chain. The strand has a spring constant of 28.8 N/m. The chain is
stretched horizontally on a frictionless tabletop to a length of 1.50 m,
and the beads at both ends are fixed in place. (a) What is the linear mass
density of the chain? (b) What is the tension in the chain? (c) With what
speed would a pulse travel down the chain? (d) The chain is set vibrating
and exhibits a standing-wave pattern with four antinodes. What is
the frequency of this motion? (e) If the beads are numbered sequentially
from 1 to 101, what are the numbers of the five beads that remain motionless?
(f) The 13th bead has a maximum speed of 7.54 m/s. What
is the amplitude of that bead’s motion? (g) If x0 = 0 corresponds to the
center of the 1st bead and x101 = 1.50 m corresponds to the center of
the 101st bead, what is the position xn of the nth bead? (h) What is the
maximum speed of the 30th bead?

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