Use dimensional analysis to determine the dispersion relation (k) for surface tension waves (up to a multiplicative
Question:
Use dimensional analysis to determine the dispersion relation ω(k) for surface tension waves (up to a multiplicative constant), which can only depend on the surface tension σ, the density ρ, and the wave number k. Find the phase velocity and the group velocity, and show that vg = 3vp/2. Describe how you could distinguish visually between gravity waves and surface waves by observing the way that individual wave crests move through a wave packet.
Step by Step Answer:
By dimensional analysis v g ddk 32k 3v p 2 Since v g v ...View the full answer
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The property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules. The cohesive forces between liquid molecules are responsible for the phenomenon known as surface tension. The molecules at the surface of a glass of water do not have other water molecules on all sides of them and consequently, they cohere more strongly to those directly associated with them (in this case, next to and below them, but not above). is not really true that a \\\"skin\\\" forms on the water surface; the stronger cohesion between the water molecules as opposed to the attraction of the water molecules to the air makes it more difficult to move an object through the surface than to move it when it is completely submersed
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