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PH 105

PH 105. Dr. Cecilia Vogel Lecture 6. OUTLINE. Natural or Normal Modes Driving force Resonance Helmholtz resonator Standing Waves Strings and tubes Longitudinal vs transverse waves. Superposition. When two disturbances (or waves) are at the same place at the same time,

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PH 105

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  1. PH 105 Dr. Cecilia Vogel Lecture 6

  2. OUTLINE • Natural or Normal Modes • Driving force • Resonance • Helmholtz resonator • Standing Waves • Strings and tubes • Longitudinal vs transverse waves

  3. Superposition • When two disturbances (or waves) • are at the same place at the same time, • total disturbance is the sum of the two. • watch impulsive waves

  4. Interference • Because of superposition, • Waves, when they meet • can add or interfere constructively • so the total is • periodic waves, when they meet • can cancel or interfere destructively • so the total is

  5. Beats • Two waves with slightly different frequency (period) go in and out of phase

  6. Interference • Waves from two source, • will have places where they interfere constructively • what does it sound like with sound? • what does it look like with light? • and other places where they interfere destructively • what does it sound like with sound? • what does it look like with light? • video

  7. Normal Modes • A normal or natural mode is • a way the system behaves when left to move naturally. • How does a pendulum behave naturally? • How does mass on a spring behave naturally? • How does string vibrate naturally? • Some systems have multiple normal modes

  8. Driving Force • You can apply a periodic driving force • a force that pushes the system periodically • Period of driving force = • Example: pushing a swing

  9. Sympathetic Vibrations • A driving force will often cause the driven system to vibrate • with the same period as the driving force. • If the driving vibrator is vibrating naturally, these vibrations are called sympathetic vibrations. • Listen to the tuning fork; • listen again when on box • box driven by tuning fork. • both emit sound

  10. Resonance • When the frequency of the driving force matches a natural frequency, • the driving force has • the vibrator is resonating • Why push a swing each time it swings? • Observe spring on and off resonance.

  11. Helmholtz Resonator • A bottle with a neck is analogous to a mass on a spring. • the air in the neck is the mass which oscillates • the volume of air in the bottle acts as a spring • Called a Helmholtz resonator • f=resonant frequency • V = volume of bottle • bigger bottle, _____ r freq (pitch) • a = neck area, l= neck length • long, skinny neck, _____ freq

  12. Closed Tube Resonances • If tube is closed at both ends • the pressure has no • there is a pressure antinode at ends • Observe slinky “pressure” hi & lo at fixed end • observe that a pressure antinode is a displacement (motion) node!

  13. Closed Tube Resonances • How can there be antinodes at both ends? • If • etc • L = • L = l • L =

  14. Resonant Frequencies of Closed Tube • L = nl/2 • n = 1, 2, 3, 4, 5, …. • Since lf = v • n shows there are many resonant frequencies

  15. Resonances of Open Tube • If tube is open at both ends, it has a pressure node at both ends • displacement __________ • analysis is similar

  16. Tube with One Closed End • If tube is closed at one end • there is a pressure _________ at that end • _______ at the other end

  17. Closed Tube Resonances • How? • If • etc • L =l/4 • L = • L =

  18. Resonant Frequencies • L = nl/4 • n = 1, 3, 5, 7, 9…. (only odd!) • Since lf = v • n odd

  19. Standing Wave in String • String is generally fixed at both ends • node at • analysis like • L = nl/2 • n = 1, 2, 3, 4, 5, …. Were measured resonant frequencies integer times f1?

  20. Standing Wave in String • Combine • Can change resonant freq’s by changing

  21. Impedance and Resonance • A reflection can occur any time there is a change in impedance. • Acoustic Impedance means difficulty of air flow • observe wave machines • There can be resonance in each part of a complex tube: L1 L2 L3

  22. Summary • Interference is the addition of waves at point where they meet • constructive interference • destructive interference • Normal modes are natural behavior • sometimes multiple natural frequencies • At resonance • driving frequency matches natural freq • driving force has a huge effect • Resonance of • Helmholtz resonator, open and closed tubes, strings

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