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atat1tata
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My book (an old copy of Halliday-Resnick) gives a proof for the fact that the wave velocity is constant in 1-dimensional transversal elastic waves, but it says nothing about other types of waves. Basically it makes a tacit assumption that all waves have constant velocity.
However it proves that the amplitude of a circular wave (a ripple in water) decreases proportionally to [tex]\frac{1}{r^2}[/tex]. I think that it assumes that the wave velocity is constant.
From another point of view if one uses cowishly the relation [tex]v^2 = \frac{T}{\mu}[/tex] one could say that, at least for an elastic circular wave, [tex]\mu[/tex] is proportional to [tex]r[/tex] and the wave velocity should vary.
As you can see I'm a bit confused and I would like to ask if someone could at least provide me with a proof of why the wave velocity is constant in water waves, 2- and 3-dimensional elastic waves and acoustic waves.
PS: I would be extremely grateful if someone could correct my English where I made mistakes in the language
However it proves that the amplitude of a circular wave (a ripple in water) decreases proportionally to [tex]\frac{1}{r^2}[/tex]. I think that it assumes that the wave velocity is constant.
From another point of view if one uses cowishly the relation [tex]v^2 = \frac{T}{\mu}[/tex] one could say that, at least for an elastic circular wave, [tex]\mu[/tex] is proportional to [tex]r[/tex] and the wave velocity should vary.
As you can see I'm a bit confused and I would like to ask if someone could at least provide me with a proof of why the wave velocity is constant in water waves, 2- and 3-dimensional elastic waves and acoustic waves.
PS: I would be extremely grateful if someone could correct my English where I made mistakes in the language
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