Man-made generation of water waves

[0pt618]

The only man-made water waves I can think of are artificial waves in specialized swimming pools. If the wavelength of the water wave is W, does the instrument generating these waves have to have dimensions on the same order as W?

In other words, if you have a small object, can you generate waves with long wavelengths?

The motivation for this question comes from a song, which have lyrics along the lines of "like a small boat, generating big/long waves..."

 

[JBA]

The wavelength is inversely proportional to the input frequency, not the size of the object generating the wave. The magnitude of the wave is a function of the energy of the object initiating the wave not the objects size. For example, a given size row boat with a 200 lb person jumping up and down at a rate of one jump per second with generate the same wavelength as that same boat with a 100 lb person jumping at the same rate; but, the heavier person will generate a larger wave (but only if in each case both people are jumping to the same height).

 

[0pt618]

Thanks JBA. Would you know any resources, such as book chapters or webpages, that sets out the physics of mechanical (man-made) water wave generation?

 

[boneh3ad]

The wavelength is inversely proportional to the input frequency, not the size of the object generating the wave. The magnitude of the wave is a function of the energy of the object initiating the wave not the objects size. For example, a given size row boat with a 200 lb person jumping up and down at a rate of one jump per second with generate the same wavelength as that same boat with a 100 lb person jumping at the same rate; but, the heavier person will generate a larger wave (but only if in each case both people are jumping to the same height).

This would be more accurate if the wave motion was decoupled from the fluid dynamics of the situation. Let's look at the boat example. This time, instead of changing the person's weight, keep the same size person and frequency but change the boat size. The larger boat is going to displace more water in the same amount of time. While the wavelength is inversely proportional to the frequency as you said above, there is a factor you left out in that a different size of object, for a given amplitude and frequency, will move more water around and likely have a different wave speed, and therefore a different wavelength.

So I therefore do believe that the wavelengths generated by an object will depend on the size of the object, and it is very likely that the wavelengths you can generate are limited to some range similar to the size of the object.

 

[JBA]

The larger boat would have larger buoyant force and therefore for the same weight individuals and jump height, it is unlikely that any significantly larger would be created. That being said, yes, size does matter when it comes to wave amplitude, i.e. even with equal impact velocities, a large cannon ball will generate a larger wave than a smaller one. The size of the wave is dependent upon the total volume of water displaced and the rate at which it is displaced.

Opt618: I do not have any information about available sources of mechanical wave generation literature; nor did a through web turn up any serious literature on wave generating machine designs (even the normally trusty Wikipedia let me down on this subject). However, I did find the below site that at least shows how one wave tank location generates it waves; and, there is some indication that this a pretty standard method of doing so (but it is definitely not an inexpensive or simple one). I hope this helps a little bit.

http://science.howstuffworks.com/engineering/structural/wave-pool5.htm