Talk:Dispersion (water waves)

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Untitled

Could someone please explain the dispersion relation, and what the hyperbolic tangent "means." thanks you.

Eh?

Phase vocoder links here (via the disambiguation page). As this is therefore a topic of potential interest to musicians, it would be helpful if a summary could be prepended to it that musicians (and bass players) can comprehend. Ireneshusband 03:46, 17 June 2006 (UTC)[reply]

This article should not link here, as the application of dispersion to water waves is not relevant to music. candlefrontin17 —Preceding comment was added at 16:46, 20 March 2008 (UTC)[reply]

approximation

why is the approximate dispersion relation w^2 = gh. is that even a dispersion relation? —Preceding unsigned comment added by 160.39.210.93 (talk • contribs) 23:08, 31 October 2007

For shallow water (small kh), the approximation is ω²=gh k², since tanh(kh) is approximately kh in this limit. So shallow water waves are not dispersive, according to linear theory. For fairly long waves, the Boussinesq approximation can be made, taking dispersive effects into account. Crowsnest (talk) 18:33, 20 March 2008 (UTC)[reply]

Typo

In the dispersion relation table I believe there is a typo which sees an upper case omega replace the usual lower case character.

Can someone please confirm I'm not missing anything, and if not, make the change? — Preceding unsigned comment added by 202.36.179.65 (talk) 22:01, 5 September 2012‎ (UTC)[reply]

No, it is not a typo, see the text above the table. The dispersion relation is ω² = [Ω(k)]², so ω = ±Ω(k). -- Crowsnest (talk) 22:26, 5 September 2012 (UTC)[reply]

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Translations of wave dispersion

Greek: κυματοδιάχυση

Is the title slightly misleading ?

I am new to this forum but would like to raise a few doubts on the practical efficacy of this article.

First of all, allow me to state that the article is quite beautifully written and very well supported. However, it is also quite misleading in the sense that it completely misses out on one of the central characteristics of waves, which is that their speed is solely dependent on the properties of the medium through which they travel. Perhaps, the article overstates one aspect of waves in water while understating others. In general, changing the frequency or amplitude of a wave will not change the wave speed, only a change in the properties of the medium will bring about a change in the speed of the wave.

For instance take the speed of sound in air as a general approximation: the speed of sound in air doesn’t depend on frequency. If the speed of sound depended on frequency the instruments at a concert would be out of sync; with the bass and treble travelling at different speeds. The whole would be very discordant. Surely, a similar case must exist in the case of water- waves? Given a shallow expanse of water with little or no variation in depth, and no variation in density, the speed of water- waves too must be dependent solely on the medium they are travelling through and not on frequency or wave length.

Ocean waves do in fact travel at a frequency (wavelength) dependent speed. But these waves are boundaries between two media not the speed of a disturbance within a medium...... Perhaps a change in the title to Dispersion (water waves) in Deep Water would better fit the article especially since the article states that waves in shallow water resemble a soliton. One of the characteristics of solitons is their constant speed.

Jms 2023 (talk) 03:43, 28 February 2023 (UTC)[reply]