Force Waves at a Rigid Termination

To find out how force waves recoil from a rigid termination, we may convert velocity waves to force waves by means of the Ohm's law relations of Eq.$\,$(4.6), and then use Eq.$\,$(4.10), and then Eq.$\,$(4.6) again:

$$\begin{eqnarray*} f^{{+}}(n) &=&Rv^{+}(n) \,\mathrel{\mathop=}\,-Rv^{-}(n) \,\ma... ...el{\mathop=}\,Rv^{+}(n-N/2) \,\mathrel{\mathop=}\,f^{{+}}(n-N/2) \end{eqnarray*}$$

Thus, force waves reflect from a rigid termination with no sign inversion:^5.2

$$\begin{eqnarray*} f^{{+}}(n) &=& f^{{-}}(n) \\ f^{{-}}(n+N/2) &=& f^{{+}}(n-N/2) \end{eqnarray*}$$