Physics 1251 The Science and Technology of Musical Sound

# Physics 1251 The Science and Technology of Musical Sound

## Physics 1251 The Science and Technology of Musical Sound

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1. Physics 1251The Science and Technology of Musical Sound Unit 3 Session 28 MWF Clarinets and Other Reeds

2. Physics 1251 Unit 3 Session 28 Clarinets et cetera What pitch (frequency) does a flute play if the length from the embouchure to the finger hole is 67.5 cm [∼26½ inches] (including end corrections) when the temperature in the tube is 37 C? f = v/2L′; v =343 + 0.6 (T-20C) v = 343 +0.6(37-20) = 343 + 0.6 (17) = 353 m/s f = 353/(2 ‧ 0.675) = 262 Hz. With no warm up: f ′ = 344/354 f = 255. Hz, Δf = f ′– f = 262 –255 = 7 Hz. ₧ = 3986 Log (255/262) = - 47¢, ∼1/4 tone ♭

3. Physics 1251 Unit 3 Session 28 Clarinets et cetera With what velocity should the flautist blow to produce a stable tone of 262 Hz if the embouchure is about 0.01 m? f = 0.2 vjet / b 262 Hz = 0.2 vjet /0.01 vjet = 262 ‧ 0.01/0.2=13.1 m/s (≈ 30 mph)

4. Physics 1251 Unit 3 Session 28 Clarinets et cetera 1′ Lecture: • Reed instruments are stopped pipes. • The clarinet has a cylindrical bore and is a stopped pipe; consequently, only odd harmonics are significant. • Conical pipes exhibit all harmonics, even in stopped pipes. • The saxophone, oboe and bassoon‒all have conical bores.

5. Physics 1251 Unit 3 Session 28 Clarinets et cetera Comparison of Flute and Clarinet Registers • Overblown flutes jump from a fundamental f1= v/2L to an octave f2 = 2f1 in the second register; an octave (2x) and a perfect fifth (3/2) f3 = 3 f1 =3 (v/2L) in the third register. • Overblown clarinets jump from a fundamental f1 = v/4L to an octave (2x) and a fifth (3/2)‒“the twelfth‒” in the second register, because only odd harmonics produce standing waves in a stopped cylindrical pipe.

6. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ Physics 1251 Unit 3 Session 28 Clarinets et cetera Reed Instruments • The reed produces a pulsation in the pressure admitted to the pipe; the pressure standing wave feeds back to control the oscillations of the reed. Standing wave frequencies Reed pulsations Feedback

7. Physics 1251 Unit 3 Session 28 Clarinets et cetera The Clarinet: Bell Body Reed The clarinet has a cylindrical bore.

8. Air flow Tonguing Physics 1251 Unit 3 Session 28 Clarinets et cetera The Single Reed 80/20The reed opens and closes like a valve, pressurizing the pipe when open, closing due to the Bernoulli effect when the air flows. Reed

9. Physics 1251 Unit 3 Session 28 Clarinets et cetera Hard and Soft Reeds 80/20A hard reed is one for which the frequency is determined by its stiffness and dimensions. A soft reed flexes easily and vibrates at the frequency of external pressure fluctuations. Soft Reeds Hard Reed: Harmonica Clarinet Oboe

10. Physics 1251 Unit 3 Session 28 Clarinets et cetera Harmonium or Reed Organ Hard or soft reed?

11. Air flow Physics 1251 Unit 3 Session 28 Clarinets et cetera The Double Reed 80/20The reed opens and closes like a valve, pressurizing the pipe when open, closing due to the Bernoulli effect when the air flows. Pressure Pulses Reed Tip

12. Physics 1251 Unit 3 Session 28 Clarinets et cetera Bassoon Reeds Double Reed The Bassoon uses a double reed, as does the Oboe and English Horn. Reed Double Reed

13. Physics 1251 Unit 3 Session 27 Flutes et cetera Bernoulli Effect • 80/20The pressure in a fluid decreases as the velocity increases. • Thus, as the air flows past the reed, it is forced closed. Bernoulli Effect

14. Pressure inverts Physics 1251 Unit 3 Session 28 Clarinets et cetera 80/20Feedback from the pressure standing wave locks the frequency of the oscillation of the reed. f2n-1 = (2n-1) v/ 4L′ Pressure wave L′ = L + 0.3 d 0.3 d

15. Physics 1251 Unit 3 Session 28 Clarinets et cetera Other Bore Shapes: Conical‒ Pressure node Pressure anti-node Pressure anti-node

16. Physics 1251 Unit 3 Session 28 Clarinets et cetera 80/20For a stopped conical pipe: fn≈ nv / 2(L′ + c) if c << λ L′ = L + 0.3 d L′ d c 0.3 d

17. Physics 1251 Unit 3 Session 28 Clarinets et cetera Why? Z changes along the length of the pipe. Weighted String Analogy

18. Physics 1251 Unit 3 Session 28 Clarinets et cetera Saxophone: Conical bore English horn: Other Reed Woodwinds: Conical bore Oboe: Conical bore Bassoon: Conical bore

19. Physics 1251 Unit 3 Session 28 Clarinets et cetera The Reed Pipes of Organs: • Conical • Voiced by Reeds • Tuned by Spring Pipe Shallot Reed Tuning Spring

20. Reed Physics 1251 Unit 3 Session 28 Clarinets et cetera Bicycle Horn

21. Physics 1251 Unit 3 Session 28 Clarinets et cetera Edge versus Reed Cylinder versus Cone

22. Physics 1251 Unit 3 Session 28 Clarinets et cetera Summary: • Reed Instruments are stopped pipes. • L′ = L + 0.3 d • f2n-1 = (2n-1) v/4L′ for stopped cylindrical pipes such as the clarinet. • fn = n v/ 2(L′+c) for stopped conical pipes such as the saxophone, oboe, bassoon, etc. • Soft reeds act as pressure valves that respond to the frequency fed back from the standing waves of the pipe.