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Sound Resonance and Wave Interference Explained

Explore natural modes, driving forces, resonance phenomena like Helmholtz resonator, standing waves in strings/tubes, and wave interference principles. Learn about superposition, beats, and how waves combine or cancel out to create sound effects. Discover the science behind sympathetic vibrations and resonant frequencies.

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Sound Resonance and Wave Interference Explained

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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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