1 / 20

Physics 1251 The Science and Technology of Musical Sound

Physics 1251 The Science and Technology of Musical Sound. Unit 1 Session 6 Helmholtz Resonators and Vibration Modes. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes. Foolscap Quiz:

destiny-hawkins
Download Presentation

Physics 1251 The Science and Technology of Musical Sound

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 1251The Science and Technology of Musical Sound Unit 1 Session 6 Helmholtz Resonators and Vibration Modes

  2. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Foolscap Quiz: What is the frequency of a simple harmonic oscillator that has a spring constant of k = 50.0 N/m and a mass m of 1.00 kg? Frequency = f = 1/(2π)√(K/m) f = 0.1592√(50.0/1.00) f = 0.1592√(50.0) = 1.13 Hz P =1/f = 1/1.13 Hz = 0.89 sec

  3. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Put seat number on the Foolscap. Do you wish to sit here “permanently?” Joe College 1/14/02 Session #1 Seat #123

  4. Physics 1251 Unit 1 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes 1′ Lecture: • A Helmholtz resonator is a simple harmonic oscillator where the mass is provided by the air in a narrow neck while the spring is provided by a volume of trapped air. • The natural frequency of a Helmholtz Resonator is given by the formula: f = [v/(2π)]√[A/ (V L)] A: area of neck v: velocity of sound in air V: volume of Bottle L: length of neck

  5. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes 1′ Lecture (cont’d.): • When an object has n masses and n springs, there are n degrees of freedom and n modes of oscillation. Often each mode has a different frequency; occasionally some frequencies are the same.

  6. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Does Air have mass and weight? How much? Density = ρ = mass/volume

  7. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Density of Air • Density = ρ = Mass/Volume • ρ = 1. 2 kg/ m3

  8. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes The “Bulk Modulus” B is the springiness of a gas. B is equal to the change in pressure (in Pa) for a fractional change in volume. B = Δp / (ΔV/V) What is the increase in pressure if I decrease the volume of trapped gas by 50%? B = 1.41 x 105 Pa. Δp = (ΔV/V) B = 0.50 (1.41 x105 ) = 70 kPa .

  9. ΔV ΔV V ΔV/V: Force: Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Air has “Springiness” F = A B ( ΔV/V) = - (A2 B/V) x 0 0.33 0.50 0 20. N 30. N

  10. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Lowest Frequency Highest Frequency Largest Volume k ∝ 1/V so f ∝ 1/√V Smallest Volume

  11. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Turbulence ⃔ ⃕ ⃔ ⃕ ⃔ ⃔ Simple Harmonic Motion of Air ⃕ Air “mass” → ⃕ ↕ Oscillation of air mass Air “spring” →

  12. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes • Two 500 ml Flasks • Same Volume • Same Length of neck • Different diameter • Same frequency? ←Smaller diameter f = 1/(2π)√[k/m] f = 1/(2π)√[(A2B/V) / (ALρ)]v= √ B/ρ f = v/(2π)√[A/ (V L)] Larger → diameter

  13. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Helmholtz Resonator • Ocarina Open holes increase area of “neck.”

  14. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Application of Helmholtz Resonator: Ported Speaker Cabinet Air “Spring” Air “mass”

  15. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Normal or Natural Modes of Oscillation

  16. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Two Masses on Two Coupled Springs Spring ———→ Mass ————→ Spring ————→ Mass ————→ Mode 1 Mode 2

  17. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes 80/20A Simple Harmonic Oscillator has only one Normal or Natural Mode of Oscillation and only one frequency of oscillation.

  18. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes 80/20The number of Normal or Natural Modes of Oscillation is equal to the number of simple harmonic oscillators that are coupled together.

  19. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes 80/20Two Normal or Natural Modes of Oscillation are called “degenerate” if they have the same frequency.

  20. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Mode Summary: • A Helmholtz Oscillator is a SHO comprised of an enclosed air volume and a narrow neck and has a single frequency. • A normal or natural mode of vibration or oscillation is one of the fundamental ways that a device can move. • The number of modes is equal to the number of simple harmonic oscillators in the system. • Degeneracy means two or more normal modes have the same frequency.

More Related