Vibrations and Waves Legacy Problem #5 Guided Solution
Problem*
Extreme waves along ocean waters, sometimes referred to as freak waves or rogue waves, are a focus of much research and study among scientists. Several merchant ships report rogue waves which are estimated to be 25 meters high and 26 meters long. Assuming that these waves travel at speeds of 6.5 m/s, determine the frequency and the period of these waves.
Audio Guided Solution
A good problem solver reads a problem carefully and identifies the known and unknown quantities, and then begins to draw upon their understanding of physics concepts and formulas in order to get from the known information to the unknown information. Here what we have are waves which are 25 meters high, that's the amplitude, I write down A equals 25 meters, and 26 meters long, I understand that to be how long the waves are or the wavelength, so I write down lambda, or wavelength, equals 26 meters. They travel at speeds of 6.5 meters per second, that's the V, as in V equals F lambda. What we're asked to determine is the frequency in the period. So one of my equations for frequency is that V equals F times lambda, that would be rearranged to look like an equation for frequency, it would be F equals V divided by lambda. Now if I wish to find the frequency, I can use this equation because I have the V, the speed, and the lambda, the wavelength. So if I go 6.5 meters per second divided by 26 meters, I would end up getting 0.25 per second, and that's the frequency, and the per second part of that means that's the frequency in units of hertz. Now if I want to find the period, and I know the frequency, I can always use the relationship that the period is the reciprocal of the frequency, that T equals 1 per F. So if I take the reciprocal of 0.25 hertz, I'll get 4.0 seconds, and that's the period.
Solution
Frequency: 0.25 Hz
Period: 4.0 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.