Wave amplitude/energy relationship problem the square of one is one?

[Chris 197]

Wave amplitude/energy relationship problem...the square of one is one!?

Hi,

1. I am trying to understand the relationship of wave amplitude and wave energy, knowing that Energy is proportional to Amplitude squared. My problem is that the proportion seems to differ for the same wave based on the unit used to define it.

For example:

a) An ocean wave with an amplitude of 1 meter seems to have a proportional energy value of 1, or a 1:1 ratio.

b) The exact same wave measured in feet (approximately 3 feet) has an energy value of 9, a 1:3 ratio.

2. I am using the equation E $$\propto$$ A²

3. It seems to me that the only answer is that you can calculate the proportional difference between two or more waves using this formula.

 

[Delphi51]

There isn't really a problem here. Energy is equal to some constants times amplitude squared. Say E = kA^2. The k has units. Its value is different if you use different units. For example for some wave you might have k = 100 J/m^2. So if the wave is 1 m high, you get
E = 100 J/m^2 * (1 m)^2 = 100 J.
In feet, you would convert k = 100 J/m^2 = 100 J/(3 ft)^2 = 11 J/ft^2
and E = 11 J/ft^2 * (3 ft)^2 = 100 J.

 

[Chris 197]

Thanks Delphi51! That was very helpful.