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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 454

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Short Answer

A rope of mass m and length L hangs from a ceiling. a. Show that the wave speed on the rope a distance y above the lower end is v = 1gy. b. Show that the time for a pulse to travel the length of the string is ∆t = 22L/g.



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Step by Step Solution

Given Information

Mass of rope: m

Length of rope: L

y is an assumed length measured from bottom of the rope.

Part a:

We know that

Where, v is speed of sound

is tension in the string

and is the linear density of the string.

, where M is mass of string of y length.

g is acceleration due to gravity


Now substituting these values in equation (1) we get,

Part b:

Now since we have the velocity as a function of length from bottom end of the rope, we can calculate time taken by wave to travel by integrating inverse of velocity over length L i.e.


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