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After learning about progressive waves, I struggle to understand what physically causes particles to move up and down in such a wave. What mechanism is actually transferring energy as these particles move up and down? Only longitudinal waves seem intuitive to me.

Furthermore, consider water waves. Do we still consider this transverse, even though the particles move in circles rather than up and down. What causes this movement? Is it true water can only be transversal due to the attraction and interactions between water molecules?

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  • $\begingroup$ Shear stress leads to the presence of transverse waves. Concerning intuition: Imagine a long thread fixed horizontally between two points. If you flick against the thread vertically at one point, a transversal disturbance spreads out. The thread deforms downwards and upwards due to the mechanical excitation instead of to the left and right because the thread "hangs together". In air, the effect does not occur because the individual air particles are not firmly connected to each other, or in other words, no shear stresses can be transmitted. $\endgroup$
    – Bulbasaur
    Commented Jul 18, 2023 at 9:34

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What physically causes particles to move up and down in [a transverse] wave ?

Think about a transverse wave in a stretched rope or a plucked string. Energy is put into the wave by the transverse movement of one or both ends, or by displacing the middle of the string and releasing it. The bonds between different parts of the rope/string mean that when one part is displaced, it pulls on the parts next to it, and so displaces them in turn. This is the mechanism for energy transfer along the rope/string. As one part of the rope/string transfers energy to other parts of the rope/string, it is at the same time pulled back towards its equilibrium position by a restoring force - in this case, the tension in the rope/string. Thus a transverse wave travels along the rope/string with a speed that depends on the tension in the rope/string and the material that it is made out of.

Do we still consider [water waves] transverse, even though the particles move in circles rather than up and down ?

Surface waves on water (or any other liquid) are a complex phenomena, and show how the simplistic division of waves into longitudinal and transverse types breaks down. As you say, surface waves are neither (or possibly both at the same time ?). Surface waves with long wavelengths are another type of wave called a gravity wave or Airy wave. Things are further complicated by the fact that at short wavelengths surface tension become the dominant restoring force rather than gravity, and the waves are now capillary waves.

Is it true water [waves] can only be transversal due to the attraction and interactions between water molecules ?

No. Longitudinal waves can travel through the body of water (rather than on the surface). This is how sound waves travel underwater.

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