Sound Waves Legacy Problem #3 Guided Solution
Problem*
Indoor pests such as mice and other rodents are sensitive to ultrasonic sound waves (sound waves above the human range of frequency detection). Some companies have produced (allegedly) rodent repellant devices that emit ultrasonic waves with frequencies of approximately 45 kHz. Assuming a speed of sound of 344 m/s, determine the wavelength of these sound waves.
Audio Guided Solution
A trip to the local hardware store will reveal that there are many products on the market which claim to use ultrasonic sound waves, which repel rodents and mice from your home. These products produce sound waves with frequencies of 45 kilohertz. The kilo in kilohertz means 10 to the third, so the frequencies of these sound waves are 45,000 hertz. They travel through air at speeds of 344 meters per second, and in this question we're asked to determine the wavelengths of these sound waves. We need to use the wave equation. The wave equation states that V equals F times lambda. We know V and we know F, and we can solve for lambda, or wavelengths, of these waves. I rearrange the equation to say wavelength equal V divided by F, and then I divide the 344 meters per second by the 45,000 hertz, and that gives me a wavelength value of .007644 meters. And I can round that to .0076 meters.
Solution
0.0076 m or 7.6 mm
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., \(\descriptive{v}{v,velocity} = 345\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 1.28 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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 Sound Waves at The Physics Classroom Tutorial.