Sound Waves Legacy Problem #26 Guided Solution
Problem*
In the Speed of Sound Lab, Anna Litical and Noah Formula partially submerge a plastic tube into a column of water. The water air interface causes the tube to be a closed-end air column. Holding a 384-Hz tuning fork above the tube, they find that they must adjust the length of air within the air column to 22.6 cm in order to force the air column into resonance vibration with the tuning fork. Determine the speed of sound in the air column.
Audio Guided Solution
This problem pertains to a very common lab which is performed in a physics class in which a long tube is placed or partially submerged within a column of water, and its length is adjusted by submerging more or less of the tube within the water, and it's adjusted until it vibrates with a loud sound as a tuning fork which is held above its open end. This is a closed-end air column lab often used to find the speed of sound within the air column. Now in this question we're told that a 384 Hz tuning fork is forcing the air in the column to vibrate, and that the air column has a length of 22.6 cm. It's a closed-end air column because there's water at one of the ends, thus forcing air at that end to not vibrate. The other end open to the atmosphere where the tuning fork is placed is actually an antinodal position in terms of the movement of the air. And so what we need to do is recognize that F1 equal 384 Hz and L equal 22.6 cm, and within that length of the air column there's one quarter of a wavelength since there's a node at one end and an antinode at the other end. So the 22.6 cm equal one quarter wavelength. What I'm looking for is the speed. So the strategy is to find the wavelength from the standing wave pattern and the length of the air column, and then to use the wave equation to calculate the speed. So 22.6 equal one quarter wavelength that I can solve for wavelength comes out to be 90.4 cm or 0.904 m. I can take this 0.904 m and multiply it by the frequency and that gives me the speed of 347.14 m per second. I can round that to three significant digits.
Solution
347 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.