What is the equation for calculating energy carried by a wave?

In summary, the conversation discusses the relationship between the amplitude and energy of a wave, as well as the exact equation for this relationship. It also mentions the energy carried by a wave defined by a Fourier series. The topic then shifts to infrastructure issues with tidal wave energy generation and potential conflicts with other uses of the ocean. It is suggested to research existing wave power extraction facilities for further information.
  • #1
yoq_bise
3
0
Hi all,
In all books I looked it is written that energy carried by a wave is proportional to its amplitudes square

i.e.
E[tex]\propto[/tex]A2, if wave equation is f(x)=Asin(wx)

but what is the exact equation?

Also if we define the wave with Fourier series

f(x)=[tex]\sum[/tex]Acos(nx)+Bcos(nx)

what would be the energy carried by this wave?
 
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  • #2
yoq_bise said:
E[tex]\propto[/tex]A2, if wave equation is f(x)=Asin(wx)

but what is the exact equation?
To be proportional, you expect [tex]E=kA^2[/tex]. k depends on the type of wave and type of medium.
Also if we define the wave with Fourier series

f(x)=[tex]\sum[/tex]Acos(nx)+Bcos(nx)

what would be the energy carried by this wave?

I suppose you meant [tex]\sum Acos(nx)+Bsin(nx)[/tex].

[tex]E=k\sum{(A^2+B^2)}[/tex]

if k is independent of frequency. Otherwise

[tex]E=\sum{k(A^2+B^2)}[/tex]
 
Last edited:
  • #3
this is a little off topic, but I'm doing a project and i need to know some infrastructure issues with tidal wave energy generation, and i don't know of any, help please?
 
  • #4
KickKat said:
this is a little off topic, but I'm doing a project and i need to know some infrastructure issues with tidal wave energy generation, and i don't know of any, help please?

Well, what other uses of the ocean are there that might be in conflict with wave energy extraction devices? And what kind of infrastructure would be necessary to convert the energy to electrical grid power, and how would you get it to the grid?

Look at the various proposals for (and some actual installed) wave power extraction facilities, and think about those issues I mentioned above...
 

What is energy carried by a wave?

Energy carried by a wave refers to the amount of energy that is transmitted through a medium as a wave passes through it. This energy can take various forms, such as mechanical, electromagnetic, or thermal energy.

How is energy carried by a wave measured?

The energy carried by a wave is typically measured in units of joules (J). The amount of energy carried by a wave is proportional to the amplitude of the wave, which is the height of the wave from the center line to the peak or trough.

What factors affect the amount of energy carried by a wave?

The amount of energy carried by a wave is affected by several factors, including the amplitude of the wave, the frequency of the wave, and the medium through which the wave is traveling. In general, waves with larger amplitudes and higher frequencies will carry more energy.

Can energy carried by a wave be transferred from one medium to another?

Yes, energy carried by a wave can be transferred from one medium to another. This is known as wave propagation. When a wave encounters a boundary between two different media, such as air and water, some of the energy in the wave is reflected back while the rest is transmitted into the new medium.

How is energy carried by a wave related to wave speed?

The speed of a wave is directly related to the amount of energy it carries. In general, waves with higher speeds will carry more energy. This relationship can be seen in the wave equation, where the speed of a wave is equal to the frequency of the wave multiplied by its wavelength.

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