A heavy rope with length L and mass M is attached to the ceiling and is...
A heavy rope with length L and mass M is attached to the ceiling
and is allowed to hang freely. (a) Find an expression for the
tension in the rope at a point a distance y from the bottom, and
use this to show that the speed of transverse waves on the rope is
independent of its mass and length but does depend on the distance
y according to the equation ?=??. (b) If L
= 3.0 m and the bottom end of the rope is given a sudden sideways
displacement, how long will it take the resulting wave pulse to go
to the ceiling, reflect, and return to the bottom of the rope?
(Hint: you will have to take an integral - a nice application of
calculus!)
Homework Answers
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A heavy rope 6.00 mm long and weighing 23.4 N is attached at one
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What is the speed of transverse waves on the rope at the bottom
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A heavy rope 6.00 mm long and weighing 23.4 N is attached at one
end to a ceiling and hangs vertically. A 0.590-kg mass is suspended
from the lower end of the rope.
Part A)
What is the speed of transverse waves on the rope at the bottom
of the rope?
Part B)
What is the speed of transverse waves on the rope at the middle
of the rope?
Part C)
What is the speed of transverse waves on the...
Problem 1 [8 pts] A uniform string of mass m and length L hangs vertically from the ceiling. (a) Find the tension in the rope as a function of distance from the lower end, and therefore determine the speed of a wave pulse as a function of position. (b) Solve by integration 2 = v(y) to determine the time it takes a wave pulse to travel the full length of the string.
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