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Learning Introductory Physics with Activities

Section 18.12 Practice - Superposition

Subsubsection Explanation Practice

Explanation 18.12.1. Wave at a Boundary.

Two strings are tied together and a wave is sent down string 1. String 1 has a linear mass density three times smaller than string 2. When the wave reaches the point where the strings are tied together and moves through string 2, you observe the wavelength. Is the wavelength in string 2 greater than, less than, or equal to the wavelength in string 1?

Subsubsection A*R*C*S Practice

A*R*C*S 18.12.2. Muscovite Sheet.

Muscovite, which as \(n = 1.56\text{,}\) or better known as mica, is a phyllosilicate mineral of aluminum and potassium. New industrial uses include being an insulator, usually for small electrical components. Fabrication of devices with mica often require high precision in the determination of the mica thickness. If a mica sheet is suspended in air and reflected light shows gaps in the visible spectrum at \(450\text{,}\) \(525\text{,}\) and \(630 \mathrm{~nm}\text{,}\) what is the thickness of the mica sheet?

Subsubsection Numerical Practice

Calculation 18.12.3. Tube of Air.

A cylindrical tube of air sustains standing waves at \(600 \mathrm{~Hz}\text{,}\) \(800 \mathrm{~Hz}\text{,}\) and \(1000 \mathrm{~Hz}\text{,}\) but at no other frequencies between \(600\) and \(1000 \mathrm{~Hz}\text{.}\) Which of the following statements are plausible here?
  1. The fundamental frequency is \(50 \mathrm{~Hz}\) and the tube is open on both ends.
  2. The fundamental frequency is \(100 \mathrm{~Hz}\) and the tube is open on both ends.
  3. The fundamental frequency is \(100 \mathrm{~Hz}\) and the tube has one open and one closed end.
  4. The fundamental frequency is \(200 \mathrm{~Hz}\) and the tube has one open and one closed end.
  5. The fundamental frequency is \(200 \mathrm{~Hz}\) and the tube is open on both ends.
  6. The fundamental frequency is \(200 \mathrm{~Hz}\) and the tube is closed on both ends.
Answer.
E., F.

Calculation 18.12.4. Speakers.

Suppose you observe that the shortest non-zero path length difference that produces constructive interference from two coherent unknown sources is \(128 \mathrm{~m}\text{.}\) What is the wavelength of the source?
At which of the following path length differences will constructive interference also occur?
  1. \(\displaystyle 64 \mathrm{~m}\)
  2. \(\displaystyle 180 \mathrm{~m}\)
  3. \(\displaystyle 256 \mathrm{~m}\)
  4. \(\displaystyle 320 \mathrm{~m}\)
  5. \(\displaystyle 512 \mathrm{~m}\)
  6. \(\displaystyle 832 \mathrm{~m}\)
  7. \(\displaystyle 3264 \mathrm{~m}\)
  8. \(\displaystyle 4096 \mathrm{~m}\)
At which of the following path length differences will destructive interference occur?
  1. \(\displaystyle 64 \mathrm{~m}\)
  2. \(\displaystyle 180 \mathrm{~m}\)
  3. \(\displaystyle 256 \mathrm{~m}\)
  4. \(\displaystyle 320 \mathrm{~m}\)
  5. \(\displaystyle 512 \mathrm{~m}\)
  6. \(\displaystyle 832 \mathrm{~m}\)
  7. \(\displaystyle 3264 \mathrm{~m}\)
  8. \(\displaystyle 4096 \mathrm{~m}\)
Answer 1.
\(128 \mathrm{~m}\)
Answer 2.
C., E., H.
Answer 3.
A., D., F., G.

References References

[1]
Numerical practice activities and the Muscovite Sheet Activity provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.