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Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.

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Relation between transverse velocity of sound and Young's modulus in solids

Usually, ultrasound measurements apply longitudinal waves, $w_L$ rather than transverse waves, $w_T$, in order to measure the longitudinal velocity through the sample. … \nabla^2 w + (\lambda + \mu) \nabla (\nabla \cdot w) \end{equation} We use the vector identity: \begin{equation} \nabla(\nabla \cdot w) = \nabla^2w + \nabla \times w \end{equation} With longitudinal waves
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