The Science Behind Tsunamis: Study the Effect of Water Depth on Wave Velocity
AbstractA tsunami is a series of waves made in a body of water, like the ocean, that can cause serious destruction when they hit the coastline. In deep water, a wave can be just a few feet high and travel very fast. As it nears the coastline, and moves into shallower water, tsunamis usually slow down, but the wave height can grow to 100 feet! In this ocean science project, you will model a tsunami and investigate how wave velocity (speed) depends on water depth. Does it match the mathematical equation for wave velocity as it depends on water depth? Tsunamis can be a destructive force of nature, but by studying how tsunamis form and how they move, better warning systems can be put into place and lives can be saved.
To investigate and model the effect that water depth has on wave velocity.
Tsunami. The word alone evokes fear and panic. On December 26, 2004, a megathrust earthquake occurred 160 kilometers (km) off the western coast of northern Sumatra, one of the islands of Indonesia, in the Indian Ocean. The magnitude 9.2 earthquake happened 30 km below mean sea level and spawned a massive tsunami that hit 14 countries. The countries that sustained the greatest damage along its coasts were Indonesia, India, Sri Lanka, and Thailand. Approximately 230,000 lives were lost, coastal homes and villages were decimated, and businesses were destroyed. The earthquake was so enormous that Earth's crust ruptured 1,200 km! Figure 1 and Figure 2 show the size of a tsunami wave and how the enormous wave can take people onshore by surprise.
Figure 1. This image shows one of the waves in the 2004 Indian Ocean tsunami hitting the shore in Thailand. Note the size of the person on the beach. The photographer of this picture died. (www.andaman.org, 2004.)
Figure 2. People onshore in Thailand surprised by a tsunami wave. (Wikipedia, 2004.)
But what is a tsunami and what does an underwater earthquake have to do with creating tsunamis? Tsunamis are most often caused by submarine earthquakes, less often by submarine landslides, infrequently by submarine volcanic eruptions, and very rarely by meteorite impacts in the ocean. A tsunami is generated when a large amount of water is displaced very quickly. When the earthquake occurred outside of Sumatra, the Indo-Australian tectonic plate moved 20 meters (m) below the Eurasian tectonic plate. This is called subduction. This caused the Eurasian plate to thrust up several meters. This earthquake also created submarine landslides. Events such as submarine earthquakes and landslides release a colossal amount of energy that is transferred to the surrounding water. An ocean wave is not moving water, but energy that is passing through water. The water particles do not move, but they transfer energy to the next particle of water. In deep water, a tsunami's energy is mostly located below the sea surface and the wave height is just a couple of meters. This is why ships on the open ocean usually don't move much when a tsunami passes beneath. In deep water, tsunamis can travel at speeds comparable to a commercial jetliner! When the tsunami moves into shallower water, however, its enormous energy is concentrated within a smaller volume. This yields waves of greater height and slower speed. However, the speed of the wave is still much faster than a human can run. The contours of the sea floor and the coastline greatly influence the tsunami wave. The height of the tsunami waves that came to shore in the 2004 Indian Ocean tsunami were between 24 and 30 m high! Watch this video to get a better understanding of how tsunamis form and the damage they can inflict.
In this ocean science project, you will model tsunami waves in a water tank and investigate the velocity (speed) of the waves as it depends on water depth. As stated above, in deeper water, the wave travels at a faster speed than in shallow water. Will this hold true even in your water tank? What is the relationship between wave velocity and water depth? Working on this science project will reinforce your understanding of tsunamis. Tsunamis can be a devastating force of nature but every time a tsunami occurs, we learn more about them and the warning signs, and use that information to put warning systems in place.
Terms and Concepts
- Megathrust earthquake
- Submarine earthquake
- Square root
- What is a tsunami and how does it form?
- Why do waves move forward?
- What causes tsunami waves to increase as they move toward shore?
- From your research, what are some of the warning signs that a tsunami might be heading to shore?
- Wikipedia Contributors. (2010, January 24). 2004 Indian Ocean Earthquake. Wikipedia: The Free Encyclopedia. Retrieved January 25, 2010.
- National Oceanic and Atmospheric Administration and National Weather Service. (n.d.). NOAA Tsunami Program. Retrieved November 9, 2020.
- Pierce, R. (2009). Maths Is Fun: Squares and Square Roots . Retrieved April 13, 2010.
For help creating graphs, try this website:
- National Center for Education Statistics. (n.d.). Create a Graph. Retrieved June 2, 2009.
Materials and Equipment
- Water tank; a 41-quart (qt.) under-the-bed type of plastic storage container works well and is likely available at your local home goods store. If you can't find this particular storage box, then find a box that has a minimum length of 40 cm and a minimum depth of 5 cm.
- Source of water that is located close to where you will be testing
- Wood, 2 inches (in.) thick x 4 in. wide x 8 in. long
- Permanent marker
- Ruler, metric
- Digital stopwatch
- Lamp; preferably a bright ceiling light directly under which you can position the water tank
- Hand towel
- Volunteer (1)
- Lab notebook
- Graph paper
- Find a well-lit location at which to perform your tests, preferably indoors. This location should be free from excess traffic. Remove any items away from the location that could be damaged by water. There might be some minor splashing from the water tank. Place the water tank on a white or light-colored surface, such as a white sheet. This will allow you to see the waves clearly. Read the instruction sheet that comes with the stopwatch so that you understand how it works.
Caution: Before you begin the experiment, review these notes:
- We strongly suggest placing the water tank directly under a ceiling light; for intance, on a white sheet on your kitchen table under a main kitchen light.
- Turn off any surrounding lights.
- Make sure the lamp and cord are always far away from the tank of and source of water.
- Be careful not to touch the lamp with wet hands. Dry your hands with the towel before handling the lamp.
- Fill the water tank with a few centimeters (cm) of water. You will first practice making and tracking waves.
- Draw a small line with the permanent marker, approximately 2.5 cm below the rim of the tank, on the outside. Draw the line on one of the shorter ends of the rectangular tank. This is the height from which you will drop the wood block. Bring in your volunteer to help you track the wave.
- Line up the bottom of the wood block at the marked line. From the marked line, drop the wood block and watch the resulting wave. Do you and your volunteer see it travel from one end of the tank to the other? Carefully bring the desk lamp over to shine light onto the tank. Try angling the light above the tank or other positions to help you track the wave.
- Once you feel comfortable creating and tracking waves, start the experiment.
- Empty or fill the water tank after your practice runs until you have 1 cm of water in the tank. Use the metric ruler for accuracy.
- Create a data table in your lab notebook, like the one shown below:
|Water Depth (cm)||Trial||Time to Travel Length of Water Tank (seconds)||Average Time Across 10 Tests||Average Time Across Water Depth Trials||Wave Velocity|
|Test 1||Test 2||Test 3||Test 4||Test 5||Test 6||Test 7||Test 8||Test 9||Test 10|
- Have your volunteer ready with the stopwatch to start timing how long it takes a wave to travel from one end of the tank to the other. Hold the bottom of the wood block at the mark on the tank. As soon as you drop the block and a wave is created, the volunteer should start the stopwatch. The volunteer should stop the stopwatch when the wave hits the other end of the tank. Record the time in the data table in your lab notebook.
Repeat step 9 nine more times to ensure more-accurate data.
- Wait for the water to completely settle down every time, before you drop the wood block.
- Hold the wood block the same way each time your drop it into the water tank.
- Record all data in the data table in your lab notebook.
- Now fill the water tank until the water depth is 2 cm. Use the ruler to confirm the water depth. Repeat steps 9–10. Record all of the data in the data table in your lab notebook.
- Fill the water tank until the water depth is 3 cm. Use the ruler to confirm the water depth. Repeat steps 9–10. Record all of the data in the data table in your lab notebook.
- Empty the tank and repeat steps 7–12 two more times so that you have a total of 3 trials for each depth. Performing 3 trials for each depth ensures that your data is reproducible and repeatable. Be sure to record all of the data in the data table in your lab notebook.
Analyzing Your Data
- Average the time data for each water depth for each trial, across the 10 tests. Record the data in the Average Time Across Ten Tests column in your lab notebook.
- Now for the Average Time Across Water Depth Trials column, average the time data across the three trials from the numbers you calculated in the previous step. Record the data in the data table in your lab notebook.
- Measure the distance between where the wave was created (the leading edge of the mark where you dropped the wood block) and the other end of the water tank. Record this data in your lab notebook (not in your data table).
- Divide the distance by the average time that it took for the wave to move from one end of the water tank to the other end for each water depth. Record this information in the data table under the Wave Velocity column in your lab notebook.
- Now plot the data. You can plot the data by hand, or you can plot your data online. For help creating plots online, try the following website: Create a Graph. Label the x-axis Water Depth and the y-axis Wave Velocity. What is the relationship between the water depth and the wave velocity? Is it a linear relationship? Does the wave velocity increase or decrease with increasing water depth? Does this result make sense to you according to the research that you have done on tsunamis?
- Equation 1, below, shows the mathematical relationship between the wave velocity in shallow water as a function of water depth. Notice the check mark next to the term g. This check mark is the mathematical sign for square root. Equation 1 states that velocity is the square root of the product of the acceleration of gravity and the water depth. If you need help understanding square roots, consult your math teacher and read the reference in the Bibliography.
Equation 1: V = √gd
- V = Velocity in meters/second (m/s)
- g = Acceleration of gravity (9.8 meters/second2)
- d = Water depth in meters (m)
- Plot wave velocity as a function of water depth, using Equation 1. How does the plot compare to the results that you got from your water tank?
Ask an Expert
- Instead of having a smooth bottom, place gravel on the bottom of the water tank. Does the uneven bottom affect the wave velocity? Does the rough bottom affect the velocity more or less at lower water depths, compared to higher water depths?
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