Sound Waves Legacy Problem #1 Guided Solution
Problem*
The speed (v) at which sound travels through air is dependent upon the temperature of the air and seems to follow the equation v = 331 m/s + 0.6 m/s/°C * T where T is the Celsius temperature of the air. Determine the speed of sound …
- On a cold day when the outdoor temperature is 4°C.
- Inside the school where the temperature is 24°C.
- On a warm day when the outdoor temperature is 38°C.
Audio Guided Solution
The speeds of sound waves are dependent upon the properties of the medium. For sound waves traveling through air, the property of the medium that affects the speed is the temperature. Here we are given an equation which expresses the dependence upon the speed of sound upon the Celsius temperature. The equation states that if we wish to calculate the speed at any given Celsius temperature, we need to take that Celsius temperature, multiply by 0.6, and then add that factor on to 331 meters per second, which happens to be the speed of waves at 0 Celsius. So at 4 degrees Celsius, I need to take the 0.6 and multiply by 4, I get 2.4, I add that on to 331, I get 333.4, and I can round that to 333 meters per second. In part B of the problem, I need to take the 0.6 and multiply it by the 24, I end up getting 14.4 meters per second. I can then add that on to the 331 meters per second and I get 345.4 meters per second and I can round that to 345. I do the same thing for 38 degrees, I add it on to 331, I end up getting 354 meters per second once I round the value.
Solution
- 333 m/s
- 345 m/s
- 354 m/s
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.