Light Waves and Colors Legacy Problem #11 Guided Solution
Problem*
The diagram at the right represents the interference pattern created by two water waves. The waves were created by two objects bobbing up and down in phase at the same frequency. Point P on the pattern is a distance of 36.9 cm from S1 and 61.5 cm from S2. Determine the wavelength (in cm) of the water waves.
Audio Guided Solution
Before I discuss the solution to this question, I'm going to call your attention to the links at the bottom of this page, which head back to the Physics Classroom tutorial, to the section on the topic of two-point source interference. This is a difficult topic, and a very visual one as well. There at the Physics Classroom, the topic and the concepts of two-point source interference are developed quite thoroughly, and it's worth a look if you're having difficulties with this question. Now, when waves from two sources meet and interfere constructively, then the distance which the wave travels from one source must be a whole number of wavelengths greater or less than the distance that it travels from the other source. Here, we know the distance to point P from source 1 and from source 2. The fact that point P is a meeting up of a crest and a crest means that point P must be a constructive interference location, and a whole number of wavelengths further from S2 than it is from S1. The fact that it's on the second antinodal line means that the whole number is the whole number 2. So I can say that the path difference is equal to 2 times the wavelength. Now, the path difference is simply the difference in distance traveled from S1 to point P compared to S2 to point P. So if I take the difference between 61.5 cm and 36.9 cm, I'll get 24.6 cm, and this is equal to 2 times the wavelength. Dividing the number by 2, I end up getting a wavelength of 12.3 cm.
Solution
12.3 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.