Vibrations and Waves Legacy Problem #12 Guided Solution
Problem*
A marine weather station detects waves which are 9.28 meters long and 1.65 meters high and travel a distance of 50.0 meters in 21.8 seconds. Determine the speed and the frequency of these waves.
Audio Guided Solution
Here we are given a boatload of information about waves passing a marine weather station, and we wish to use the information to determine the speed and the frequency. I read that these waves are 9.28 meters long. That's the wavelength, the length of the wave. And they're 1.65 meters high. That's the amplitude, or maybe one-half the amplitude, but it really doesn't matter here because it won't be relevant to solving the problem. We're told that they travel a distance of 50 meters in 21.8 seconds, and I understand that the speed of a wave is the distance traveled divided by the time it takes to travel that distance. The distance traveled per unit of time would therefore be the 50 meters divided by the 21.8 seconds. So using the distance and the time, I've just determined the speed of the waves. It comes out to be about 2.2936 meters per second, and I can round that to three significant digits. Now finally I need to determine the frequency of these waves, and I'm going to have to use the wave equation to do that. The wave equation is V, or speed, is equal to frequency times wavelength, F times lambda. So I'm given the speed, or at least I've calculated the speed, it's currently on my calculator, as 2.2936 meters per second, and I'm given the wavelength as 9.28 meters. So if I divide the V by the wavelength, I can get the frequency of the waves. That would be the 2.2936 meters per second divided by the 9.28 meters, and that comes out to be 0.2472 per second, or 0.2472 hertz, and that's the answer to what's the frequency.
Solution
speed = 2.29 m/s
frequency = 0.247 Hz
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.