Light Waves and Colors Legacy Problem #7 Guided Solution
Problem*
Determine the wavelength of the microwave radiation emitted …
- By a microwave oven (f = 2.45x109 Hz).
- By a cordless phone (f = 5.8x109 Hz).
Audio Guided Solution
Here we wish to calculate the wavelength of waves created by two objects in part A by a microwave oven and in part B by a cordless phone. A microwave oven emits waves with a frequency of 2.45 times 10 to the 9th hertz. In order to calculate the wavelength of these waves we need to use the wave equation V equal F times lambda where V is the speed, F is the frequency given here, and lambda is the wavelength. Rearranging to solve for lambda we would have lambda equal V divided by F. V, the speed of microwave radiation, is 2.998 times 10 to the 8th meters per second. Dividing that by the frequency of 2.45 times 10 to the 9th hertz gives us the wavelength in units of meters. It comes out to be 0.1224 meters. We can round that to three significant digits such that the answer is 0.122 meters. Repeating the process for the cordless phone means that we have to take the speed of light again, 2.998 times 10 to the 8th meters per second, and divide it by the frequency of the waves emitted by the cordless phone. Divide it by 5.8 times 10 to the 9th hertz. Doing so will give us the wavelength in units of meters and it comes out to be 0.0517 meters. We can round that to two significant digits such that it is 0.052 meters.
Solution
- 0.122 m or 122 cm
- 0.052 m or 5.2 cm
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.