# What is the difference between wave speed and transverse speed?

Here is the equation of a wave

(1) $\,y(x,t)=2\sin(4x-2t)$

What is the wave speed?

What is the maximum speed perpendicular to the wave's direction of travel (transverse speed)?

I understand both questions and know how to determine the wave speed but the textbook never mentioned anything about transverse speed until now.

Can someone please explain what exactly transverse speed is in detail and the derivation of the formula? The only thing that comes to mind is the velocity of SHM since it is basically asking how fast the particle or element is moving vertically as the wave propagates.