Light Waves and Colors Legacy Problem #8 Guided Solution
Problem*
Determine the wavelength of the infrared carrier wave transmitted by a television remote control at 38 kHz.
Audio Guided Solution
As you're watching television, you press a button on the remote control pad. You're sending an infrared ray signal to the television. This infrared radiation has a frequency of about 38 kilohertz. Terms of hertz, that can be the same as 3.8 times 10 to the 4th hertz. Here we wish to calculate the wavelength of these waves. That means we need to use the wave equation, V equals F times lambda. Rearranging that for lambda, which is the wavelength, we have lambda equal V divided by F. Now, substituting in values of V of 2.998 times 10 to the 8th meters per second and a value for F of 3.8 times 10 to the 4th hertz, we could solve for lambda. We end up getting 7889.47 meters, and we can round that to two significant digits, such it becomes 7.9 times 10 to the 3rd meters.
Solution
7900 m (rounded from 7889 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.
Read About It!
Get more information on the topic of Light Waves and Colors at The Physics Classroom Tutorial.