= Solution
A characteristic <wave impedance> relates an effort-like quantity to its conjugate flow-like quantity in a single travelling wave: for a mechanical wave these are <force> and <velocity>, and their product is <power>. The sign depends on the propagation and <force> conventions. Use the transverse <force> transmitted towards increasing $x$, $F=-T\Psi_x$. A rightgoing <travelling wave> $\Psi=f(x-vt)$ has transverse <velocity> $u=\Psi_t=-v\Psi_x$, so
$$
\boxed{Z=F/u=T/v=\sqrt{T\rho}},\qquad [Z]=\mathrm{kg\,s^{-1}}.
$$
This is the positive <characteristic impedance of a stretched string>. A leftgoing component has $F/u=-Z$ with the same <force> orientation. Its units differ from pressure-based <acoustic impedance> because it uses <force>, rather than <force> per area.
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