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Chapter 21: Superposition

Chapter 21: Superposition. The combination of two or more waves is called a superposition of waves. Applications of superposition range from musical instruments to the colors of an oil film to lasers.

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Chapter 21: Superposition

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  1. Chapter 21: Superposition The combination of two or more waves is called a superposition of waves. Applications of superposition range from musical instruments to the colors of an oil film to lasers. Chapter Goal: To understand and use the idea of superposition. In this chapter you will lean: ● Understand how standing waves are generated ● Apply the principle of superposition ● Understand how waves cause constructive and destructive interference ● alculate the allowed wave lengths and frequencies of standing wave

  2. What do the colors of an oil film?

  3. Reading assignments • 21.1 The principle ofSuperposition • 21.2 Standing waves • 21.3 Transverse Standing waves • 21.5 Interference in one dimension • 21.6 The Mathematics of Interference

  4. Stop to think 21.1 page 635Stop to think 21.2 page 641Stop to think 21.3 page 645Stop to think 21.5 page 655Stop to think 21.6 page 658 • Example 21.1 page 638 • Example 21.2 page 641 • Example 21.5 page 643 • Example 21.6 page 645 • Example 21.8 page 649 • Example 21.10 page 653

  5. The principle of Superposition • When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacements due to each individual wave.

  6. Standing Waves

  7. Standing Waves on a String

  8. When a wave pulse on a string reflects from a hard boundary, how is the reflected pulse related to the incident pulse? • Shape unchanged, amplitude unchanged • Shape inverted, amplitude unchanged • Shape unchanged, amplitude reduced • Shape inverted, amplitude reduced • Amplitude unchanged, speed reduced

  9. Standing wave Ex: there are two waves: The resultant wave function is: Notice, in this function, does not contain a function of (kx±ωt). So it is not an expression for a traveling wave

  10. Standing wave on a String • A standing wave can exist on the string only if its wavelength is one of the values given by • F1=V/2L fundamental frequency. • The higher-frequency standing waves are called harmonics, ex. m = 2, second harmonics m=3 third harmonics Node Antinode

  11. Stop to think: A standing wave on a string vibrates as shown at the figure. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. which standing-wave pattern is produced Answer: a

  12. Standing Sound Waves • Open-open or closed-closed tube m =1,2,3……

  13. Open-closed tube

  14. EXAMPLE 21.4 Cold spots in a microwave oven QUESTION:

  15. The mathematics of Interference D = D1 + D2 = • The phase: • The phase difference is • Constructive interference: ΔΦ = m(2π) • Perfect destructive interference ΔΦ = (2m + 1 )π • For identical source ΔΦo=0, so 2πΔx/λ = m(2π) is constructive interference. 2πΔx/λ = (2m+1) π is destructive interference.

  16. Important Concepts

  17. Interference in thin film Two factors influence interference: Possible phase reversals on reflection Differences in travel distance The total phase difference is ΔΦ = m(2π) constructive ΔΦ =( m+1/2) 2π destructive

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