Sound Waves Legacy Problem #12 Guided Solution
Problem*
During a Variety Show practice, Jake plucked a string on his guitar, sending vibrations through it in both directions. The string is pulled to a tightness of 220 N and has a mass density of 0.013 kg/m. Determine the speed with which vibrations travel through the string.
Audio Guided Solution
The speeds at which vibrations and waves travel through strings and wires and ropes is dependent upon the properties of those strings, wires, and ropes, and the two main properties which are of importance are how tight the rope is being pulled and the mass density or linear density of that rope or string or wire. So here we have a guitar string and the vibrations are traveling through it. We know how tight it's being pulled, that's the 220 Newtons, and we know the linear mass density as 0.013 kilograms per meter. Now the equation can be found on the overview page for this set of problems, it simply goes like this. The speed is equal to the square root of the ratio of tension to linear density. So I need to take the 220 Newtons and divide it by the 0.013 kilograms per meter, and once doing that I need to take the square root of the whole thing and I end up getting 130.0887 meters per second. I can round that to two significant digits and get 130 meters per second.
Solution
130 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.