Light Waves and Colors Legacy Problem #9 Guided Solution
Problem*
- Determine the frequency of electromagnetic radiation which would have a wavelength of 1.0 mile (1.6 km).
- What part of the electromagnetic spectrum does this fall within?
Audio Guided Solution
Here we�re asked to calculate the frequency of an electromagnetic wave which is a wavelength of one mile. That�s equivalent to 1.6 kilometers. So we have a lambda wavelength and we�re looking to calculate a frequency and as usual we know that the speed at which light travels is 2.998 times 10 to the 8th meters per second. So I must use the wave equation V for speed is equal to f times lambda where f is the frequency. Rearranging to solve for frequency I would have f equal V divided by lambda. Now my lambda needs to be in units of meters so I�ll convert the 1.6 kilometers to 1,600 meters. Now I take that wavelength and I substitute it into the denominator of the equation f equal V divided by lambda and I can solve for f. It comes out to be 187,375 hertz and I can round that to two significant digits such that it becomes 1.9 times 10 to the 5th hertz. Now I can look up in some sort of resource like a textbook or the physics classroom tutorial to find out what portion of the EM spectrum this is and I�ll find that it is in the radio wave section of the electromagnetic spectrum.
Solution
- 1.9x105 Hz
- Radio wave spectrum
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., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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 Light Waves and Colors at The Physics Classroom Tutorial.