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Standing Waves

Standing Waves. Physics 202 Professor Lee Carkner Lecture 7. PAL #6 Wave Energy. How do you find linear density? v = f l = ( t / m ) ½ or m = t /f 2 l 2 Get frequency from function generator f = Get wavelength by measuring on string l = Get tension from hanging weights

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Standing Waves

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  1. Standing Waves Physics 202 Professor Lee Carkner Lecture 7

  2. PAL #6 Wave Energy • How do you find linear density? • v = fl = (t/m)½ or m = t/f2l2 • Get frequency from function generator • f = • Get wavelength by measuring on string • l = • Get tension from hanging weights • hanging mass is 225g so t = mg = (.225)(9.8) = 2.205 N • m = • Velocity = fl • v = (22.54)(1.5) =

  3. Exam #1 Friday • About 1/3 multiple choice • Study notes • Study Quizdom questions • Look at textbook “Checkpoint” questions • About 2/3 problems • Study PAL’s and SuperPALS • Study old homework • Do new practice homework questions • Try to do this with just equation sheet • Need (real) calculator and pencil

  4. Standing Waves • The two waves will interfere, but if the input waves do not change, the resultant wave will be constant • Nodes -- • Antinodes -- places where the amplitude is a maximum (only place where string has max or min displacement) • The positions of the nodes and antinodes do not change, unlike a traveling wave

  5. Standing Wave Amplitudes

  6. Equation of a Standing Wave • If the two waves have equations of the form: • Then the sum is: • The amplitude varies with position • e.g. at places where sin kx = 0 the amplitude is always 0 (a node)

  7. Nodes and Antinodes • For kx = np, sin kx = 0 and y = 0 • Node: x=n (l/2) • For kx=(n+½)p, sin kx = 1 and y=2ym • Antinode: x=(n+½) (l/2) • Antinodes also occur every 1/2 wavelength, but at a spot 1/4 wavelength before and after the nodes

  8. Resonance Condition • Standing waves occur due to resonance • When do you get resonance? • You must have: • An integer number of “loops” • Since each “loop” is half a wavelength l = 2L/n where n = 1,2,3,4,5 …

  9. Resonance? • Under what conditions will you have resonance? • Solve for n, must be integer • v = (t/m)½ = lf • Can find new l in terms of old l and see if it is an integer fraction or multiple

  10. Harmonics f=(nv/2L) • For a string of a certain length that will have waves of a certain velocity, this is the frequency you need to use to get strong standing waves • The number n is called the harmonic number • For cases that do not correspond to the harmonics the amplitude of the resultant wave is very low (destructive interference)

  11. Generating Harmonics • Many devices are designed to produce standing waves • e.g., • Frequency corresponds to note • e.g., • Can produce different f by • changing v • Changing L

  12. Next Time • Test #1 • For Monday, December 5 • Read 17.1-17.4 and do webassign homework

  13. What kind of string propagates waves the fastest? • Heavy and tight • Heavy and loose • Light and loose • Light and tight • We can’t know wave speed without knowing the input frequency

  14. How would you modify the wave generator to input the maximum amount of energy? • Increase frequency, increase amplitude • Increase frequency, decrease amplitude • Decrease frequency, increase amplitude • Decrease frequency, decrease amplitude • Input energy is independent of frequency and amplitude

  15. What kind of string transmits energy the fastest? • Heavy and tight • Heavy and loose • Light and loose • Light and tight • All strings transmit energy at the same rate

  16. Consider a wave traveling along a string that can be combined with three otherwise identical waves with phase shifts of 0.5p, 1.0p, and 1.9p radians. Rank the resulting wave by amplitude, largest first. • 0.5p, 1.0p, and 1.9p • 1.9p, 1.0p, 0.5p • 1.0p, 0.5p, 1.9p • 1.9p, 0.5p, 1.0p • 0.5p, 1.9p, 1.0p

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