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

2. Physics 1251Unit 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 ♭ ₧ = 3986 Log (255/262) = - 47¢, ∼1/4 tone ♭

3. Physics 1251Unit 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 v jet / b 262 Hz = 0.2 v jet /0.01 v jet = 262 ‧ 0.01/0.2=13.1 m/s (≈ 30 mph)

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

5. Physics 1251Unit 3 Session 28 Clarinets et cetera Comparison of Flute and Clarinet Registers Overblown flutes jump from a fundamental f 1 = v/2L to an octave f 2 = 2f 1 in the second register; an octave (2x) and a perfect fifth (3/2) f 3 = 3 f 1 =3 (v/2L) in the third register. Overblown flutes jump from a fundamental f 1 = v/2L to an octave f 2 = 2f 1 in the second register; an octave (2x) and a perfect fifth (3/2) f 3 = 3 f 1 =3 (v/2L) in the third register. Overblown clarinets jump from a fundamental f 1 = 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. Overblown clarinets jump from a fundamental f 1 = 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. Physics 1251Unit 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. 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. ♩ ♪ ♫ f 1 f 2 f 3 f 4 f 1 f 2 f 3 f 4 fn fn ~ ~ Reed pulsations Standing wave frequencies Feedback

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

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

9. Physics 1251Unit 3 Session 28 Clarinets et cetera Hard and Soft Reeds 80/20 A 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. A soft reed flexes easily and vibrates at the frequency of external pressure fluctuations. Hard Reed: Harmonica Soft Reeds ClarinetOboe

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

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

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

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

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

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

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

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

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

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

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

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

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

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