Education if the wavelength of a set of waves is...

if the wavelength of a set of waves is 20 feet long, how deep is the wave base?


In this blog post we will be answering the question of “What is the wavelength of a set of waves that has a wave base depth of 20 feet?” You can learn more about wavelengths and wave bases by reading on.

We’re going to have to get into some physics here, so you might want to take notes if you’re just tuning in. The waves we are looking at have a wavelength that is 20 feet, which means they will travel (on average) 20 feet from one peak to another before collapsing. This is also known as a wave period, one cycle, or the time it takes for the wave to complete one up-and-down motion. So the bigger question is “How often will these waves go up and down in a certain distance?” This is known as frequency, and since we’re looking at how deep a wave base is, we will need to convert from wavelength to frequency. In doing so, you can see that there are 49.9 waves per second of these 20 foot long waves.

wavelength 1625133584
globe, earth, space @ Pixabay

This tells us that if we had a pile of sand down there that was 20 feet deep, every second it would be pushed up 49.9 inches. You can see how this would work out in a concrete wave base that is 20 feet deep, and it matches up with what we know of waves in a concrete wave pool, which is also 20 feet deep:

In order to figure out the frequency of our waves, we need to know more about wavelengths. A wavelength is the distance between two peaks of a wave. This means that the peak height between two up-and-down motions will be twice as tall as the wavelength of the waves suggests. In this case, that means that every 20 foot long wave will complete one cycle in 1/49.9 second or 1.55 seconds** (this was a rough estimate).

wavelength 1625133591
megatron, colour, temperature @ Pixabay

Now, we need to figure out the total energy of a set of waves with a wave base that is 20 feet deep. The total energy is equal to the square of the amplitude multiplied by the frequency. Our frequency is 49.9, and we’re looking at waves with a wavelength of 20 feet, so our amplitude would be 49.9^2 x 20 = 9769.8 feet per second as a basis for calculating the total energy or power radiated by these waves (also known as electromagnetic radiation).

If we want to figure out the total energy per second, we need to multiply by the number of waves in a certain period of time. That period is 1.55 seconds, so our total energy is going to be 49.9^2 x (20)(1.55) = 142695.4 watts per second. This is a very high number, and it means that these waves are incredibly powerful and have a lot of potential for causing damage or injury if you are close enough to them!

Note that this was an estimate for how long it would take those waves to complete one cycle. This was only done in order to continue the math problem; 4/49 = 0.00458 seconds = 1.55, so one complete cycle is actually 1.54 seconds (1/55 of a second). This was done based on the wavelength and wave base being 20 feet.

If you want to see some more wave power from a similar size wave base, check out our short movie.

wavelength 1625133594
rainbow, atmospheric optical phenomena, bow shaped strip lighting @ Pixabay

We hope that this blog post answered your question about the wavelength of waves with a wave base of 20 feet. If you have other questions involving more complex topics, like how sound behaves over long distances, we will be adding those to our blog soon. Enjoy!

Wave Motion Photography Style: Coastal Fantasy Location: Ocean Beach The waves are beautiful here by my house.

Editor Team
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