I was surprised to find that sea waves can reach speeds more than 50 kmh !! - needing around 90kmh winds for extended periods. This is about the maximum recorded, but there does not seem to be a speed limit for them. I guess a nuclear bomb might make an even faster wave.
Thankyou exchemist for your pointer on restoring force. The stronger response within the medium from compressibility makes sense too. I have read a little more but can't say that I really understand what is happening. My problem is that I thought that wave speed is determined by the properties of medium - this is what I read about waves.
Seismic sea pressure waves can travel at 760 km/h, sound waves at 5,400 km/h and surface waves - seemingly no speed limit except available force. The gravitational restoring force returns the surface waves to equilibrium - as in a pendulum effect (now I see what you mean about those waves - I think you are saying that the upward movement is slowed by gravity and therefore limits transverse speed - although it will also work in reverse when going back down towards the equilibrium !) but the medium is still capable of transmitting waves at different speeds.
Gravity is working at 90 degrees in all cases. What is the difference between these waves that allows them different speeds through the same medium?
If you cannot see that compressing water is a lot more difficult than lifting it, then this discussion is not going to get much further.
A transverse water wave simply requires you to displace a bit of water upwards. It then tends to fall back under gravity and as it does so it causes the next bit of water to be pushed up in turn, etc. Whereas a sound wave involves physically compressing the water, like compressing a spring. Gravity does not come into it. The restoring force is a lot higher and the wave travels a lot faster.
For surface waves in water there are two relations determining the speed:-
For shallow water c=√(gd) where d is depth of the water and g is the acceleration due to gravity.
For deep water however, it depends on wavelength, λ, as well as g, but not on depth: c= √(gλ/2π). When the speed depends on wavelength the medium is said to be dispersive. (This is true of light waves in glass for instance and is why refraction of blue light is more marked than for red light).
For sound waves, c = √(K/ρ), where K is the bulk modulus .i.e. the stiffness or resistance to compression and ρ is density.
Edited by exchemist, 11 July 2019 - 03:50 PM.