Light Waves and Colors Legacy Problem #12 Guided Solution
Problem*
Water waves with a wavelength of 7.8 cm are created in a ripple tank by two in-phase sources bobbing up and down at the same frequency. The waves form an interference pattern in the space surrounding the sources. A point on the fourth nodal line is a distance of 58.2 cm from the nearest source. Determine the distance from this same point to the furthest source.
Audio Guided Solution
Before I discuss the solution to this question, I want to call your attention to the links that you see at the bottom of this audio help page. Links lead back to the physics classroom and discuss the topic of two-point source interference. The concepts related to this question are discussed quite thoroughly, and they're worth a look, particularly if you're having troubles with the topic. You are told that water waves with a wavelength of 7.8 centimeters are created by two sources within a ripple tank. As in all two-source wave interference patterns, there will be a collection of nodal and antinodal lines produced within the medium. Here a point on the fourth nodal line is a distance of 58.2 centimeters from the nearest source. That's what we would call S1P, the distance from the nearest source to the point. What we wish to calculate is the distance S2P, the distance from the point to the furthest source. Now the fact that they've told me that it's the fourth nodal line tells me that M is equal to 3.5. So the difference in distance traveled from the nearest source to the point compared to the farthest source to the point is 3.5 times the wavelength. So if I multiply 3.5 times 7.8, I get 27.3 centimeters, telling me that the furthest source is 27.3 centimeters further from the point than the nearest source. So if I wish to find this distance, I simply add 27.3 centimeters to the 58.2 centimeters that's given, and that gives me 85.5 centimeters.
Solution
85.5 cm
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., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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 Light Waves and Colors at The Physics Classroom Tutorial.