A tsunami is a high-speed sea wave of seismic origin created by "an underwater earthquake, landslide, or volcanic eruption"(Johnston, 2001). A shallow water wave is a water wave in which the wavelength is larger than the water height, or ocean depth (Banks, 1998). Since humans are concerned with a tsunami primarily at the shore, where the water is not deep, tsunami are explored as a shallow water wave. That is, people are most concerned with the height of a wave as it hits shore. Tsunami will be discussed in the context of water depth, wave velocity, period, wavelength and energy.
The wavelength, velocity and period of a shallow ocean wave are related by the direct variation equation L = CT, where L = wavelength, C = velocity, and T = period (Bryant, 2005). This is an example of a linear relation between velocity and period. Period or velocity may also be expressed as a ratio of the other two quantities. Students may be asked to find any one of the three variable quantities, provided the other two.
A square root function that models tsunami velocity as a function of water depth is
v = (gD)1/2, where g = 9.8m/s2 and D = water depth. Alternatively, this can be a quadratic model to find the depth of water if the wave velocity is known: D = v2 / g (Abbott, 2004, Banks, 1998). The energy of a water wave, particularly a tsunami, can be modeled as a function of wave... [continues]
Cite This Essay
(2013, 01). Maths in Every Day Life. StudyMode.com. Retrieved 01, 2013, from http://www.studymode.com/essays/Maths-In-Every-Day-Life-1391878.html
"Maths in Every Day Life" StudyMode.com. 01 2013. 2013. 01 2013 <http://www.studymode.com/essays/Maths-In-Every-Day-Life-1391878.html>.
- MLA 7
"Maths in Every Day Life." StudyMode.com. StudyMode.com, 01 2013. Web. 01 2013. <http://www.studymode.com/essays/Maths-In-Every-Day-Life-1391878.html>.
"Maths in Every Day Life." StudyMode.com. 01, 2013. Accessed 01, 2013. http://www.studymode.com/essays/Maths-In-Every-Day-Life-1391878.html.