Indeed all the particles have the same amplitude of vibration in both transverse and longitudinal waves.

The exception being standing waves, which are a combination of waves. Standing waves produce nodes and anti-nodes, nodes being point of zero amplitude, and anti-nodes being points of maximum amplitude.

The equation of a standing wave is as follows (it is formed by adding the wave function of 2 compatible waves):
$A=\left[A_{o}\sin\left(kx-\phi\right)\right]\sin\left(ωt-\phi\right)$

The term $\left[A_{o}\sin\left(kx-\phi\right)\right]$ represents the variation of amplitude with distance.

The question asked in your book may very well be referring to standing waves

[![enter image description here][1]][1]

Here is a visualization of standing waves to help explain it better, the red dots are nodes, and the points of maximum amplitude are anti-nodes. The faded red and blue waves show the waves that combined to form the standing wave.

  [1]: https://i.sstatic.net/ICXk7.gif