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Sect. 11-11: Wave Reflection & Transmission. Waves can be reflected from objects. Two waves can interfere with each other. 2d & 3d waves have wave “fronts”:. Law of Reflection (Plane Waves). Sect. 11-12: Interference (Superposition). 2 waves , similar wavelengths
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Sect. 11-11: Wave Reflection & Transmission • Waves can be reflected from objects. • Two waves can interfere with each other.
2d & 3d waves have wave “fronts”:
Sect. 11-12: Interference (Superposition) • 2 waves , similar wavelengths • Spatial variation at different times. • Constructive: “In Phase” • Destructive: “Out of Phase”
Principle of superposition: In a spatial region where 2 waves overlap, the resultant wave displacement algebraic sum of the amplitudes
Sect. 11-13: Standing Waves • Standing waves: When incoming & reflected waves interfere, standing waves can be set up. • Antinodes: Positions of maximum amplitude (constructive interference). • Nodes: Positions of minimum amplitude (destructive interference). • Only certain frequencies (or wavelengths) are allowed for standing waves!
Fundamental or Natural or Resonant Frequencies Frequencies at which (large amplitude) standing waves are produced. • String: Has many resonant frequencies. • Unlike spring-mass system, which has only one!
Standing waves on a string of length L. • Still have: v = λf • Recall, v is fixed by properties of the string. v = [FT/(m/L)]½ • The standing wave frequency f = (v/λ)or, alternatively, the wavelength λ = (v/f) is fixed by the string length L! • We need to fit the wavelength λ into the length L. • We’ll focus on λ for standing waves.
General: String, length L, with both ends fixed, for standing waves we must have an integer multiplenof (½)λfit into lengthL: L = (½)nλn, n = 1, 2, 3, 4, … The only allowed wavelengths are: λn = (2L)/n , n = 1, 2, 3, 4, … • Still have: v = λf with v fixed by the string properties v = [FT/(m/L)]½ The only allowed frequencies (harmonic frequencies) are: fn = (v/λn) = (½)n(v/L) f1 = (½)(v/L) fundamental frequency fn = nf1 , n = 1, 2, 3, 4, … (Example 11-14)
