Wave motion in a transverse wave I was learning about wave motion and how in transverse waves, each particle executes SHM up and down. If that is the case, how is it so that energy is still transferred onto the next particle? The logical answer should be that it disturbs the other particle, but if it moves up and down how does that happen?
 A: It depends on the type of wave. In the derivation of waves in a string, we come to the equations:
$$\frac{\partial ^2 y}{\partial t^2} = \frac{|\mathbf T|}{\rho} \frac{\partial ^2 y}{\partial x^2}$$
$$\frac{\partial ^2 x}{\partial t^2} = \frac{1}{\rho} \frac{\partial  T}{\partial x}$$
The first one is the transverse wave as such, propagating in the $x$ direction.
But the second equation shows some movement also in the $x$ direction. As the tension is almost constant ($\frac{\partial  T}{\partial x}$ is small), that oscillatory movement is very small compared to the transverse one.
Also for water waves, besides the transverse (up and down) movement there is also some horizontal one, as shown here.
A: In the case of transverse waves, the oscillations are at right angles to the direction of propagation of the wave. The wave itself is the transfer of energy from one point to another. Say the wave moves to the right (e.g., x-direction). Then the particles in the medium of the wave are moving "up and down" (y-direction) only. There does not need to be particle motion from "left to right". There is however energy being transferred from left to right.
