Purchase Solution

A ring on an vibrating string

Not what you're looking for?

Ask Custom Question

We put a small ring of mass m on the long (infinite) string. The ring slides without friction. How does the ring move, when we send by a string the sine wave? (I need mathematical equation of moving.) How does the wave scatter on the ring? (I need the amplitude of scattering waves, or reflection coefficient R).

Please provide a mathematical procedure (differential equations) -some steps to show me how can we find the solution of this problem. And also some limits (when m goes against 0 or infinity) are welcome (not necessary).

See the attached file.

Purchase this Solution

Solution Summary

The physics of this problem is explained in detail. The problem is reduced to straightforward algebra.

Solution Preview

Let's denote the local height of the string as y(x). The derivative of y(x), dy/dx, is assumed to be small and this is thus approximately the angle of the string with the positive x-direction.

If you forget about the ring for a moment, you should have no difficulties deriving the wave equation for the string. If you focus on a small piece of the string at position x of length dx, then the force exerted by the on this piece is:

T [dy/dx(x+dx)-dy/dx(x)]= T d^2y/dx^2 dx (1)

where T is the tension of the string.

By Newton's second law this must equal

rho dx d^2y/dt^2 (2)

where rho is the ...

Purchase this Solution

Free BrainMass Quizzes
Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

The Moon

Test your knowledge of moon phases and movement.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.