Vibrations and Waves Legacy Problem #9 Guided Solution
Problem*
Logan, Cassie and Abbey are doing the Pulse Speed Lab. Logan and Cassie stand 6.8 m apart and stretch a zinc-coiled snakey between them. Logan introduces a pulse into the snakey at his end. Using a stopwatch, Abbey measures that it takes 15.1 seconds for the pulse to travel to Cassie's end and back two times. They then repeat the experiment with a copper-coiled snakey stretched the same distance and find that pulses travel back and forth two times in 16.9 seconds.
- Determine the speed of the pulse in the zinc-coiled snakey.
- Determine the speed of the pulse in the copper-coiled snakey.
Audio Guided Solution
A good problem solver will read a problem carefully, developing a mental picture of what's going on, identify the known information and the unknown quantity, and then search for a formula that relates these known to unknown quantities. Here what's going on is three students are doing a lab, and a wave is traveling, or at least a pulse is traveling, from one student 6.8 meters down to the other students and then back, and it does this two times. So the distance that this pulse is traveling is 6.8 meters times four, times four because it goes down to the other end and back, and then it does it again, down to the other end and back. So the down to the other end part is 6.8 meters, and we have to do that times four because of that distance is traveled four times. So in order to determine the speed of these pulses, we simply say the speed is the distance divided by the time, and the distance here is 6.8 times four, or 27.2 meters, and if I divide that by 15.1 seconds, I'll get the speed through the zinc-coiled slinky, or snaky rather, and that comes out to be 1.8013 meters per second. I can round that to three significant digits. Now for the copper-coiled snaky, it's just the 27.2 meters distance divided by the 16.9 seconds, and that comes out to be 1.6095 meters per second, and I can round that also to three significant digits.
Solution
- 1.80 m/s
- 1.61 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., \(\descriptive{v}{v,velocity} = 12.8 \unit{\meter\per\second}\), \(\descriptive{λ}{λ,wave length} = 4.52 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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.