Vibrations and Waves Legacy Problem #6 Guided Solution
Problem*
Tsunamis are much different than rogue waves. While rogue waves and other waves are generated by winds, tsunamis originate from geological events such as movements of tectonic plates. Tsunamis tend to travel very fast. A tsunami generated off the coast of Chile in 1990 is estimated to have traveled approximately 6200 miles to Hawaii in 15 hours. Determine the speed in mi/hr and m/s. (Given: 1.0 m/s = 2.24 mi/hr)
Audio Guided Solution
Students of physics typically use the so-called wave equation P equal F times lambda so often that they think that in order to calculate the speed you need to know the frequency in the wavelength. But here there's no frequency given and no wavelength and they ask us to calculate the speed. The 6,200 miles is the distance traveled by a tsunami wave in 15 hours and when it comes to wave speed by definition it's defined as the distance traveled per unit of time. So the 6,200 miles divided by the 15 hours would give us a wave speed. When I do that calculation 6,200 divided by 15 I get 413.33 miles per hour. I can round that to two significant digits and it becomes 410 miles per hour. Now once the wave speed is determined in units of miles per hour we can determine the same quantity wave speed in units of meters per second by simply taking the given converting information and using it to convert to meters per second. That conversion would involve dividing by 2.24 in order to get from miles per hour to meters per second. When doing so I get 184.5238 meters per second and I can round that to two significant digits such that it becomes 180 meters per second.
Solution
410 mi/hr or 180 m/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = 12.8 \unit{\meter\per\second}\), \(\descriptive{λ}{λ,wave length} = 4.52 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Vibrations and Waves at The Physics Classroom Tutorial.