[McQueen (OP)]

Would a wave created by a stone thrown into a pond and a wave created by a stick drawn through the water of the pond have the same velocity?

I am guessing that in both cases the  waves that were created would have the same velocity. 

My reasoning is as follows, imagine a van standing still and blowing the its horn. The sound would travel at a certain fixed velocity of about  343 m/s. Now imagine that the van is moving and the same horn is blowing,  although the sound would  change frequency depending on whether it is moving towards or away from you, a higher frequency in the former case and a lower frequency in the latter case, the velocity with which the sound travels would remain the same.  However, although the velocity with which the sound travels in all three scenarios would remain unaffected, the wave -length would also change, getting shorter in the former case and longer in the latter case


Now imagine that the Van is supercharged and can actually move at a speed faster than sound , what would happen to the sound of the horn in this case?  When the (hypothetical) van  passes through the air it creates a series of pressure waves in front of it and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound and, as the speed of the object increases, the waves are forced together, or compressed, because they cannot get out of the way of each other. Eventually they merge into a single shock wave, which travels at the speed of sound. So the sound of the horn becomes part of the bang!

Thus, even under extreme conditions, the velocity of a wave is dependent on the properties of the medium through which it is travelling.

[Colin2B]

Would a wave created by a stone thrown into a pond and a wave created by a stick drawn through the water of the pond have the same velocity?


I am guessing that in both cases the  waves that were created would have the same velocity. 

Not necessarily. The speed of waves in water is dependant on their wavelength. If the created waves have the same wavelength then their speed relative to the water (but not necessarily to the shore/observer) will be the same.

My reasoning is as follows, imagine a van standing still and blowing the its horn. The sound would travel at a certain fixed velocity of about  343 m/s. .................

The analogy does not work because sound waves in air (but not all gasses) are non dispersive i.e. all wavelengths travel at the same speed relative to the air.
Note again, however, that if the medium is moving relative to the observer (or vise versa) then the measured speed of sound will not be 343m/s.

[McQueen (OP)]

Colin2B : Not necessarily. The speed of waves in water is dependant on their wavelength. If the created waves have the same wavelength then their speed relative to the water (but not necessarily to the shore/observer) will be the same.

 I was hoping that I would not have to comment! But anyway here goes. A change in wavelength does not mean a change in  velocity although it does indicate a change in frequency. I think you can check this out in any text book and get the same answer. n.b. spelling mistake for dependent. 

Colin2B: The analogy does not work because sound waves in air (but not all gasses) are non dispersive i.e. all wavelengths travel at the same speed relative to the air.

What analogy ? Under what conditions are sound waves  dispersive ?

Colin 2B ; Note again, however, that if the medium is moving relative to the observer (or vise versa) then the measured speed of sound will not be 343m/s.

I wonder if you are at all aware that the velocity you are referring to namely 343 m/s is approx 10⁷m/s slower than the speed of light. (In case you are not paying much attention that is ten million times slower than the speed of light) At these speeds relativistic effects do not come into contention, they are for all purposes non-existent. So why  keep harping on this particular aspect of waves ?

[yor_on]

hmmm, a stick drawn in water? How about a plank, me pressing it down in the water from a speeding motorboat :) Do you think the wave I build up there in front of the plank will be faster than the same wave made by me standing still?  If not, why? As for Collins answer, better check this McQueen before deciding he is wrong 'hyperphysics' - Ocean Waves - Ocean Waves 

[Colin2B]

A change in wavelength does not mean a change in  velocity although it does indicate a change in frequency. I think you can check this out in any text book and get the same answer.

The subject here is waves in water and no reputable physicist would state that "A change in wavelength does not mean a change in  velocity".
Similarly there are no reputable textbooks that would make this mistake.
I would suggest some reliable textbooks, but the link provided by yor_on is reliable "The velocity of idealized traveling waves on the ocean is wavelength dependent"

hmmm, a stick drawn in water? How about a plank, me pressing it down in the water from a speeding motorboat

Another example is the bow wave of a boat, the wavelength is proportional to the speed of the boat.

What analogy ?

Analogy, comparison,  call it what you will, you were attempting to draw conclusions about water waves from sound waves and this is not valid. Ocean waves are gravity waves, sound waves are compression waves and they behave differently. In particular their speed wavelength relationship is different so you drew the wrong conclusion.

Under what conditions are sound waves  dispersive ?

CO2 is one example. There are other gasses and gas mixtures.

I wonder if you are at all aware that the velocity you are referring to namely 343 m/s is approx 10⁷m/s slower than the speed of light. (In case you are not paying much attention that is ten million times slower than the speed of light) At these speeds relativistic effects do not come into contention, they are for all purposes non-existent. So why  keep harping on this particular aspect of waves ?

Quite aware thank you. However, in case you are the one not paying attention, the reference here is not to special or general relativity, but to Galilean relativity. Far from being non-existent the effects of this are very important and are often overlooked by people who have not studied waves. Note the quote from the link provided by yor_on
"..........the speed of the progressing wave with respect to stationary water - so any current or other net water velocity would be added to it."
The same is true of sound waves, and means that the measured velocity of waves travelling in a medium depends on the observer.

[McQueen (OP)]

Yor on : hmmm, a stick drawn in water? How about a plank, me pressing it down in the water from a speeding motorboat Do you think the wave I build up there in front of the plank will be faster than the same wave made by me standing still?  If not, why?

Pardon me for stating the obvious Yor on but if you are standing still there would be no wave.  Still I get the gist of what you are saying namely that if you say step of a boat onto a plank and create a wave, would that wave travel at the same velocity as the wave made by the plank being pressed down while the boat was towing it at speed?  But obviously the ocean is a far more complicated scenario to generalise about, which considerably increases the difficulty.  For instance look at the following question:

Suppose that two waves each with a different wavelength are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A.

a) one-ninth             b) one third              c) the same as       d) three times larger than

The answer surprisingly in view of what has been stated about the velocity of a wave being dependent only on wavelength is :

The medium is the same for both of these waves ("the same container of nitrogen gas"). Thus, the speed of the wave will be the same (c). Alterations in a property of a wave (such as wavelength) will not affect the speed of the wave. Two different waves travel with the same speed when present in the same medium.

What I can gather from this statement is that the numerous topological and other features affecting waves in an ocean give rise to different forms of the medium, causing different velocities.  For instance in the article referred to by you in hyperphysics,  The nature of the wave changes with depth, thus a surface wave would have different characteristics than deeper waves.  Of course gravity also plays a huge part as the depth of the water increases.

But here is another example:

Compared to a 440 Hz sound wave, a 880 Hz sound wave will travel

A. half as fast
B. the same speed
C. twice as fast
D. four times as fast

Answer: B
 
Thus perhaps the statement that I had made regarding the fact that the velocity of a wave is dependent on the properties of the medium that it is travelling through should be altered when referring to Ocean waves  to the definition given by the hyperphysics website referred to as:

It will be presumed that ocean waves obey the basic wave relationship c= frequency x wavelength , where c is traditionally used for the wave speed or "celerity". The term celerity means the speed of the progressing wave with respect to stationary water - so any current or other net water velocity would be added to it.

From what I can gather from the above equation it is apparent that  if either the frequency or the wavelength changes the velocity remains constant. Under practical conditions however, waves at the surface of the Ocean are dependent solely on wavelength, longer wavelengths travelling faster.  I stand corrected.

[evan_au]

waves at the surface of the Ocean are dependent solely on wavelength, longer wavelengths travelling faster. 

There is another vitally important case, which is tsunamis.

The velocity of a tsunami can be calculated by obtaining the square root of the depth of the water in metres multiplied by the acceleration due to gravity (approximated to 10 m/s²).

In open ocean, a tsunami can travel at around 800km/h, while in shallow water it slows to around 80km/h.
See: https://en.wikipedia.org/wiki/Tsunami#Characteristics

[yor_on]

:) np McQueen

When it comes to the speed of sound it is the same, that is correct.
And it's interesting, but it seems also a question of what differs sound waves from water waves. Sound waves are compression waves created from the forces molecules exert on each other, which manifests as pressure.

" In water, there are two basic mechanisms that usually cause such waves: gravity, which dominates most of the larger wave phenomena (such as ocean waves); and surface tension, which causes the much smaller ripples in water. It turns out that in both of these cases the waves have what we call a dispersion, meaning that different-sized waves travel at different speeds. Actually, gravity waves travel faster the larger they are, while the opposite is the case for capillary (surface tension) waves. This is why such waves have no single speed. You correctly pointed out that sound waves are compression waves. Surface waves are not, however, transverse waves in the ordinary sense. Liquids cannot carry transverse waves "inside the bulk"; in fact this is one of the definitions of the difference between a solid and a liquid. Instead, the surface wave lives on a boundary between two different materials (e.g. air and water)." (by TheSumOfAllPeanuts)

When it comes to a gas then that too is about molecules in a atmosphere, as I see it.

[McQueen (OP)]

yor_on: " In water, there are two basic mechanisms that usually cause such waves: gravity, which dominates most of the larger wave phenomena (such as ocean waves); and surface tension, which causes the much smaller ripples in water. It turns out that in both of these cases the waves have what we call a dispersion, meaning that different-sized waves travel at different speeds. Actually, gravity waves travel faster the larger they are, while the opposite is the case for capillary (surface tension) waves. This is why such waves have no single speed.

Thanks for demonstrating that this is a pretty complicated environment that is being discussed.  In the same way your statement that 'liquids cannot carry transverse waves..' is only partially true when applied to ocean waves. Ocean waves can be  both longitudinal and transverse. Technically,  they're a special category, as you had stated , called surface waves. Due to the fact that there is  zero shear strength in water,  pure transverse waves  die out extremely quickly. Transverse waves can only survive because the water in an ocean wave does not move with the wave itself -- each molecule of water travels in a clockwise circle  giving its neighbors a push. This push increases the local pressure in the water, which allows the wave to become deeper/higher. Gravity then tries to flatten out this difference in amplitude in other words it acts as the returning force for the transverse wave and the process is repeated. This is  a transverse wave.

On another level, I think that broadly speaking ( considering the ocean very broadly speaking)  the medium does govern the velocity of the wave. In general water depth and gravity are the main factors affecting wave formation. The  group velocity for Deep Water Waves is 1/2 the phase velocity while the  group velocity for Shallow Water Waves is equal to the phase velocity.  But again this is more or less going around in circles since there are so many other factors that are involved when considering ocean waves.

[Colin2B]

.........Gravity then tries to flatten out this difference in amplitude in other words it acts as the returning force for the transverse wave .......
.....this is more or less going around in circles

Ocean surface waves are more correctly classified as orbital waves - although often loosely called transverse. They are a combination of transverse and longitudinal motion as the water moves in a circular motion also going not only up and down but slightly back and forth from trough to crests and back.
Because gravity is the returning force of the mass of water in the crests the harmonic motion of the wave is similar to that of a pendulum and the period remains constant irrespective of depth, which is why wavelength varies with speed in c=fλ.
As you say, there are many factors affecting the propagation of ocean waves, which is why we need to be careful when making comparisons.

......Instead, the surface wave lives on a boundary between two different materials (e.g. air and water)." (by TheSumOfAllPeanuts)

LOL, "TheSumOfAllPeanuts"
I might as well throw out all my oceanography lecture notes and (expensive) textbooks with you around!