The impedance for mechanical waves is defined as the ratio between the force wave and velocity wave and in general takes the form

For transverse waves in a string with linear mass density (kg/m) and tensionThe second animation shows the case Z_{1}/Z_{2} = 2,
i.e., the incident wave is in a heavier string. There is no sign reversal
in the reflected wave in this case. The transmitted wave has an amplitude
larger than the incident wave. This does not mean amplification in wave
energy. (Why not?)

The third animation shows reflection at a fixed end (Z_{2} =
infinity) and fourth animation shows reflection at a free end (Z_{2
}=
0).

**Reflection of pulse wave at an impedenace discontinuity
when Z_1/Z_2 = 0.5.**

`> `**with(plots):**
**animate((exp(-(x-t)^2)-1/3*exp(-(x+t)^2))*Heaviside(-x)+2/3*exp(-4*(x-.5*t)^2)*Heaviside(x),x=-10..10,t=-10..10,frames=50,color=red,numpoints=200);**

**When Z_1/Z_2 = 2.0.**

`> `**with(plots):**
**animate((exp(-(x-t)^2)+1/3*exp(-(x+t)^2))*Heaviside(-x)+4/3*exp(-.25*(x-2*t)^2)*Heaviside(x),x=-10..20,t=-10..10,frames=50,color=red,numpoints=200);**

**When Z_2 = infinity. (Fixed end)**

`> `**with(plots):**
**animate((exp(-(x-t)^2)-exp(-(x+t)^2)),x=-10..0,t=-10..10,frames=50,color=red,numpoints=200);**

**When Z_2 = 0. (Free end)**

`> `**animate((exp(-(x-t)^2)+exp(-(x+t)^2)),x=-10..0,t=-10..10,frames=50,color=red,numpoints=200);**

`>`