Velocity of surface water wave

[woepriest]

Im trying to find the velocity for the surface wave on water. Its like when you throw a pebble on a small lake and there's waves.

My book tells me that all mechanical wave follows this

V = √((elastic property)/(inertial property))

But water is not compressable and this wave is a longatuidal wave I believe. I am just stuck as to where to start.

 

[Hootenanny]

Im trying to find the velocity for the surface wave on water. Its like when you throw a pebble on a small lake and there's waves.

My book tells me that all mechanical wave follows this

V = √((elastic property)/(inertial property))

But water is not compressable and this wave is a longatuidal wave I believe. I am just stuck as to where to start.

Try here: http://physics.nmt.edu/~raymond/classes/ph13xbook/node7.html

The expression shown there can fairly easily be derived from the equations of motion for an incompressible, inviscid fluid.

 

[astrokreng]

Firstly, it is important to note that the velocity of a surface water wave can vary depending on various factors such as wind speed, water depth, and wave amplitude. However, there are some basic principles that can help us understand and calculate the velocity of a surface water wave.

As mentioned in your book, the velocity of a mechanical wave is determined by the ratio of two properties: the elastic property and the inertial property. In the case of a surface water wave, the elastic property refers to the water's surface tension, which is the force that holds the water molecules together at the surface. The inertial property, on the other hand, is the mass of the water that is being displaced by the wave.

Based on these properties, we can use the following equation to calculate the velocity of a surface water wave:

V = √(gλ/2π)

where V is the velocity, g is the acceleration due to gravity, and λ is the wavelength of the wave.

This equation assumes that the water is deep enough for the wave to be considered a deep-water wave, meaning that the depth of the water is greater than half the wavelength of the wave. In this case, the velocity of the surface water wave is directly proportional to the square root of the wavelength.

However, if the water is shallow, meaning that the depth is less than half the wavelength, then the velocity is given by:

V = √(gd)

where d is the water depth.

In conclusion, the velocity of a surface water wave can be calculated using the equation V = √(gλ/2π) or V = √(gd), depending on the depth of the water. It is also important to consider other factors such as wind speed and wave amplitude when determining the velocity of a surface water wave.