Consider the one-way wave equation ut + uz = 0 on the interval (-1,3) and for t> 0 with the following two sets of initial conditions: 1- if |2 <1, u(2,0) = (5) otherwise, and u(1,0) = e-52. (6) (a) Use the forward-time forward-space me: ,n+1 +-u + 0, k h with right-point boundary condition unti where IM = 3 to compute an approx- imation to the solution at several (up to 40) time steps. Use h = 0.02 and 1 = k/h = 0.8. Demonstrate numerically (plot the solution) the instability of the scheme and show that the instability appears sooner with the less smooth initial data.
(b) Comment on the localization of the onset of instability for initial data (5) and give an estimate of the expected growth rate of the instability per time step.
(c) Using the left boundary condition u(-1) = 0, write a stable scheme and compute the corresponding approximation for data sets (5) and (6). Plot the approximations at representative time steps. Use again h = 0.02 and 1 = k/h=0.8. =

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sound is invisible, but sometimes we can feel it. when a kettle-drum is thumped with a stick that time the tight drum skin moving up and down very quickly for some time and then it pumped sound waves into the air. loudspeakers also work in a similar manner.

components of a speaker:

electromagnet

in order to translate an electrical signal into an audible sound, an electromagnet is used in looudspeakers

  suspension

suspension is used to   center the voice coil in the gap of the magnet and it exerts a restoring force to keep it there. suspension is used to limits the maximum mechanical excursion of the diaphragm and voice coil.

voice coil

voice coil is a coil of wire which is attached to the apex of a loudspeaker cone. it provides the motive force to the cone by the reaction of a magnetic field to the current passing through it.

cone

in a   loudspeaker, a   thin, semi-rigid membrane attached to the voice coil, which moves in a magnetic gap due to which it vibrates   and produced sound. it is known as diaphragm and it can also be called a cone, though not all speaker diaphragms are cone-shaped.

surround

surround is also known as front suspension. surround is used to join the cone to the chassis. together with the suspension it controls the cone excursion, and it is also used to   determine how energy which is   travelling through the cone is absorbed, and how the speaker limits when it reaches the ends of its travel.

dustcap

dustcap is used to protect the voice coil from dust and dirt. it is a part of the cone.

how speaker work

the outer part of the cone is fastened to the outer part of the loudspeaker's circular metal rim. the inner part is fixed to   voice coil that sits just in front of a permanent magnet . when loudspeaker is hooked up to a stereo, electrical signals feed through the speaker cables into the coil. it will convert the coil into an electromagnet magnet . when electricity flows back and forth in the cables, the electromagnet either repels or attract the permanent magnet. this moves the coil back and forth, and it pull and push the loudspeaker cone. like a drum skin vibrating back and forth, the moving cone pumps sounds out into the air.in this way loudspeakers works.

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month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

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