Light Waves and Colors Legacy Problem #5 Guided Solution
Problem*
Mr. H catches the news on 780 AM, which broadcasts at 780. kHz. Determine the wavelength of these radio waves.
Audio Guided Solution
AM radio stations in the United States broadcast signals in the kilohertz range. A 780 AM station broadcasts at 780 kilohertz. These radio waves are light waves which travel at the speed of 2.998 times 10 to the 8th meters per second. Here we are to determine the wavelength of the 780 kilohertz radio waves. We can use the wave equation, v equal f lambda, where v is the speed, f is the frequency, and lambda is the wavelength. Rearranging to solve for lambda becomes lambda equal v divided by f. v, 2.998 times 10 to the 8th meters per second, divided by the f of 780 times 10 to the 3rd hertz, gives us a value for lambda, which is 384.359 meters, and we can round that to three significant digits.
Solution
384 m
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.
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