  Pulsar winds have longstanding problems in energy conversion and pair cascade
processes which determine the magnetization $\sigma$, the pair multiplicity
$\kappa$ and the bulk Lorentz factor $\gamma$ of the wind. We study induced
Compton scattering by a relativistically moving cold plasma to constrain wind
properties by imposing that radio pulses from the pulsar itself are not
scattered by the wind as was first studied by Wilson & Rees. We find that
relativistic effects cause a significant increase or decrease of the scattering
coefficient depending on scattering geometry. Applying to the Crab, we consider
uncertainties of an inclination angle of the wind velocity with respect to the
radio beam $\theta_{\rm pl}$ and the emission region size $r_{\rm e}$ which
determines an opening angle of the radio beam. We obtain the lower limit
$\gamma\gtrsim10^{1.7}r^{1/2}_{\rm e,3}\theta^{-1}_{\rm pl}(1+\sigma)^{-1/4}$
($r_{\rm e}=10^3r_{\rm e,3}$ cm) at the light cylinder $r_{\rm LC}$ for an
inclined wind $\theta_{\rm pl}>10^{-2.7}$. For an aligned wind $\theta_{\rm
pl}<10^{-2.7}$, we require $\gamma>10^{2.7}$ at $r_{\rm LC}$ and an additional
constraint $\gamma>10^{3.4}r^{1/5}_{\rm e,3}(1+\sigma)^{-1/10}$ at the
characteristic scattering radius $r_{\rm c}=10^{9.6}r^{2/5}_{\rm e,3}$ cm
within which the `lack of time' effect prevents scattering. Considering the
lower limit $\kappa\gtrsim10^{6.6}$ suggested by recent studies of the Crab
Nebula, for $r_{\rm e}=10^3$ cm, we obtain the most optimistic constraint
$10^{1.7}\lesssim\gamma\lesssim10^{3.9}$ and
$10^{6.6}\lesssim\kappa\lesssim10^{8.8}$ which are independent of $r$ when
$\theta_{\rm pl}\sim1$ and $1+\sigma\sim1$ at $r_{\rm LC}$.
