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0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

18. Waves & Sound

Wave Interference

2:39 minutes

Problem 25

Textbook Question

(I) If a soap bubble is 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume that n = 1.35.

Verified step by step guidance

Identify the given values: thickness of the soap bubble (t = 120 nm) and the refractive index of the soap bubble (n = 1.35).

Understand that the phenomenon described is thin-film interference, which occurs due to the constructive interference of light waves reflecting off the front and back surfaces of the thin film.

Use the formula for constructive interference in thin films: \(2nt = m\lambda\), where \(m\) is the order of the interference (typically the first order, m=1, is considered for maximum reflection), \(n\) is the refractive index, \(t\) is the thickness of the film, and \(\lambda\) is the wavelength of light.

Solve for \(\lambda\) using the equation \(\lambda = \frac{2nt}{m}\). Plug in the values: \(n = 1.35\), \(t = 120 \text{ nm}\), and \(m = 1\).

Calculate the wavelength \(\lambda\) that corresponds to the first order of maximum constructive interference, which will be the wavelength most strongly reflected.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thin Film Interference

Thin film interference occurs when light waves reflect off the two surfaces of a thin film, such as a soap bubble. The reflected waves can interfere constructively or destructively depending on the film's thickness and the wavelength of light. This phenomenon is responsible for the colorful patterns seen in soap bubbles.

Wavelength and Refractive Index

The refractive index (n) of a material affects how light travels through it, altering the effective wavelength of light within the medium. For a soap bubble with a refractive index of 1.35, the wavelength of light in the film is shorter than in a vacuum. This change is crucial for determining which wavelengths are most strongly reflected.

Constructive Interference Condition

Constructive interference occurs when the path difference between two reflected light waves is an integer multiple of the wavelength. For a soap bubble, the condition for constructive interference is given by 2nt = mλ, where n is the refractive index, t is the thickness of the film, m is an integer, and λ is the wavelength in a vacuum. This relationship helps identify the wavelengths that will be most prominently reflected.

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Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.

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Sketch the shape of the string at the end of 6.0 s.

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Textbook Question

Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.39. For what frequencies does their sound at the speakers produce constructive interference?

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Textbook Question

Two out-of-phase radio antennas at x=±300 m on the x-axis are emitting 3.0 MHz radio waves. Is the point (x, y) =(300 m, 800 m) a point of maximum constructive interference, maximum destructive interference, or something in between?

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Textbook Question

Two loudspeakers emit sound waves of the same frequency along the x-axis. The amplitude of each wave is a. The sound intensity is minimum when speaker 2 is 10 cm behind speaker 1. The intensity increases as speaker 2 is moved forward and first reaches maximum, with amplitude 2a, when it is 30 cm in front of speaker 1. What is The amplitude of the sound (as a multiple of a) if the speakers are placed side by side?

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Open Question

In the following figure, two interfering waves are drawn at some instance in time.

a. Indicate the regions on the graph where constructive interference occurs.
b.Indicate the regions on the graph where destructive interference occurs.

Two sinusoidal waves with amplitudes