In this lectures, we have attempted to

understand how waves are propagating on a string.

The reason why we selected a string as a medium is because string is the simplest case.

Okay, we found that if we have two different string, different thickness,

then how much wave is transmitted and reflected totally depends

on the characteristic impedance of these two string, Z_1 and Z_2.

So reflection and transmission is totally

determined by characteristic impedance of two media.

That's first message.

We have to understand. And the second message,

we have conveyed by examining driving point impedance.

That is a simply how much velocity

are experienced upon the force applied to the string.

So if you have infinite string,

the driving point impedance turns out to be same as characteristic impedance.

There is no imaginary punch.

However,

if you have perfectly reflected the boundary over there,

and if the length scale of this string is L,

then driving point impedance has only imaginary part

proportional to characteristic impedance but scaled

by interesting formula that is cotangent kL.

And kL, is of course,

the ratio between length,

finite length scale and wavelengths.

So the finiteness of

this length scale has to be seen by the wavelengths.

And next video, we'll show the one-dimensional wave equation,

one-dimensional wave which is propagating not on

a stream but in the medium like L and water.

And we will figure out how these concepts will

again to be applied to the compressible fluid in a one-dimensional pipe case.

Week 1 Summary Video