Vibrations and Waves Legacy Problem #10 Guided Solution
Problem*
Sachi is rock'n to her favorite radio station - 102.3 FM. The station broadcasts radio signals with a frequency of 1.023 x 108 Hz. The radio wave signal travel through the air at a speed of 2.997 x 108 m/s. Determine the wavelength of these radio waves.
Audio Guided Solution
The big equation in waves is the so-called wave equation. It's v equal f times lambda. In this problem, we read of a student that is listening to a radio station, which is broadcasting signals at 1.023 times 10 to the 8th hertz. That's the frequency of the waves. The speed at which these waves travel through the air is 2.997 times 10 to the 8th meters per second. That's the v, or speed of the waves. So if I wish to calculate the wavelength, I need to use the equation v equal f times lambda, where lambda is the wavelength. I need to rearrange it to solve for lambda. Lambda would be equal to v divided by f. That's 2.997 times 10 to the 8th divided by 1.023 times 10 to the 8th. When I do that, I end up getting on my calculator 2.9296 meters, and I can round that to four significant digits, such that it becomes 2.930 meters.
Solution
2.930 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., \(\descriptive{v}{v,velocity} = 12.8 \unit{\meter\per\second}\), \(\descriptive{λ}{λ,wave length} = 4.52 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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.