  The frequency dependence of pulse width is studied for 150 normal pulsars,
mostly selected from the European Pulsar Network, for which the 10\%
multifrequency pulse widths can be well fit with the Thorsett relationship
W_{10}=A\nu^{\mu}+W_{\rm 10, min}. The relative fraction of pulse width change
between 0.4~GHz and 4.85~GHz, \eta=(W_{4.85}-W_{0.4})/W_{0.4}, is calculated in
terms of the best-fit relationship for each pulsar. It is found that 81 pulsars
(54\%) have $\eta<-10$\% (group A), showing considerable profile narrowing at
high frequencies, 40 pulsars (27\%) have $-$10\%$\leq\eta\leq 10$\% (group B),
meaning a marginal change in pulse width, and 29 pulsars (19\%) have
$\eta>10$\% (group C), showing a remarkable profile broadening at high
frequencies. The fractions of the group-A and group-C pulsars suggest that the
profile narrowing phenomenon at high frequencies is more common than the
profile broadening phenomenon, but a large fraction of the group-B and group-C
pulsars (a total of 46\%) is also revealed. The group-C pulsars, together with
a portion of group-B pulsars with a slight pulse broadening, can hardly be
explained using the conventional radius-to-frequency mapping, which only
applies to the profile narrowing phenomenon. Based on a recent version of the
fan beam model, a type of broadband emission model, we propose that the diverse
frequency dependence of pulse width is a consequence of different types of
distribution of emission spectra across the emission region. The geometrical
effect predicting a link between the emission beam shrinkage and the spectrum
steepening is tested but disfavored.
