Physics 1251 The Science and Technology of Musical Sound

1. Physics 1251The Science and Technology of Musical Sound Unit 3 Session 30 MWF The Timbre of Wind Instruments

2. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments What is the physical difference between a Cornet, Trumpet and Flugel Horn? The fraction of the horn that is cone/cylinder/flare. • Trumpet – most cylindrical • Cornet -- more conical • Flugel Horn – most conical Trumpet Flugel Horn Cornet

3. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 1′ Lecture: • The pitch of a wind instrument is determined by the length and shape of its air column. • The effective length of the air column is controlled with holes, valves and slides. • Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. • The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument.

4. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Transverse Flute 80/20The flute is driven by air flow against the edge of the embrochure hole. 80/20A pressure node exists at the open hole. Air flow Embrochure

5. Air flow Tonguing Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 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. 80/20A pressure anti-node exists at the reed. Reed

6. Air flow Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 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. 80/20A pressure anti-node exists at the reed. Pressure Pulses Reed Tip

7. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments The Lip Valve 80/20Brass instruments are played by the player’s lips that form a lip valve. 80/20A pressure anti-node exists at the player’s lips. Louis Armstrong – trumpet (1901-1971)

8. 6fO 5f1 6f1 5f1 5fO 5f1 4f1 4fO 4f1 3f1 3fO 3f1 3f1 2f1 2fO 2f1 fO f1 f1 f1 f1 Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Comparison of Wind Instruments f Pedal Tone fo = (1+ξ)v/4(L+c) L f1 = v/2L f1 = v/4L f1 = v/2(L+c) Other Woodwinds Flute Clarinet Brass c

9. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Open Cylinder Np – Np fn = nf1 f1 = v/2L Stopped Cylinder Ap – Np f2n-1 = (2n-1)f1 f1= v/4L Stopped Cone Ap – Np fn = nf1 f1= v/2(L+c) Stopped Combination Ap – Np fn = nf0f0= (1+ξ)v/4(L+c) Comparison of Wind Instruments (cont’d.) fo = (1+ξ)v/4(L+c) L f1 = v/2L f1 = v/4L f1 = v/2(L+c) Other Woodwinds Flute Clarinet Brass c

10. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 80/20In the flute, feedback from the acoustic standing wave locks the frequency of the oscillation if the edge tone is near the fundamental frequency. Displacement wave fedge = 0.2 vjet /b fn = n v/ 2L; fedge≈ fn

11. Pressure inverts Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 80/20IIn reed instruments, feedback 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

12. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 80/20Brass Instruments are stopped pipes. • The player’s lips produce a displacement node (pressure antinode) at the mouthpiece. • A displacement anti-node (pressure node) exists at the bell. Winton Marsalis Trumpet

13. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Feedback from Resonaces • 80/20The pitch of a wind instrument is determined by the influence on the jet/reed/lip-valve of feedback from the pressure/displacement standing waves in the pipe.

14. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Wind Instruments • A jet produces a fluctuating air flow, while a reed or the lips produce pressure pulsations, the frequencies of which are controlled by feedback from standing waves in the horn. Standing waves in horn Flow fluctuations or Pressure pulsations Feedback

15. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Effect of Excitation • The mode of excitation of the horn significantly influences the harmonic recipe of the air column. • The harmonics will only be as strong as the excitation of the jet/reed/lip-valve.

16. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Embouchure Lip Valve

17. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments The Mouthpiece Cup Volume 80/20The Cup Volume and the diameter of the constriction leading to the back bore are the most important factors in determining the frequency spectrum of the mouthpiece. Diameter

18. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Driven Pipe Vibration Recipe Pipe Spectrum A Mouthpiece Spectrum A Driven Pipe Spectrum A Frequency

19. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Effect of the Pipe • A pipe is three dimensional; therefore, 3-D modes of oscillation are possible in the pipe. • 80/20Only those modes with frequency above a Cut-off Frequency fc will exist in the pipe. f > fc for propagation.

20. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Modes of Vibration of a Column of Air (0,0) D (1,0) (2,0) Cut Off Frequency fc = qn m v/D; for f < fc no propagation q00 = 0; q10 = 0.59; q20 = 0.97

21. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Effect of Modes on Spectrum • More modes implies more intensity. • Most influential in high f harmonics. • Shape and relative diameter of pipe influence modes. • Thus, a square organ pipe has a different timbre than does a round organ pipe because of the modes.

22. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Reflections from the array of holes in a woodwind affect the relative strength of the high frequency harmonics in the pipe. Displacement wave Reflections from holes (closed and open)

23. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Effect of Holes on Transmission • Larger holes have greater effect. • A “high pass filter:” Low frequencies tend to be reflected more and high frequencies transmitted more. • The holes make a “brighter” sounding instrument.

24. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Reflections from joints and imperfections affect the relative strength of the high frequency harmonics in the pipe. Reflections

25. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Filtering of Wind Instrument Sound • The vagaries of transmission of the various frequency components in the pipe produce a filtering effect on the frequency spectrum of the sound. Transmission through horn

26. f1 f2 f3 f4 ♩ ♪ ♫ fn ~ ~ Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Radiation of Sound from Wind Instruments • The radiation characteristics of the bell “shape” the harmonic recipe and strongly influence the timbre of the instrument. Radiation Characteristics

27. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments 80/20The diameter of the mouth and the flare rate of the bell determine the radiation characteristics of brass instruments. • The larger the bore diameter, the more intense the low frequency harmonics. • The more rapid the flare, the more the low frequencies are reflected, and thus, the more high frequency harmonics are radiated. Trumpet Cornet Flugel Horn

28. x Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Exponential Horn The Bell a = ao exp(m x)+ b 80/20m is called the “flare constant.” Larger m means more rapid flare.

29. a x Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Bessel Horns The Bell a = ao e-(εx) +b 80/20Called “Bessel Horns” because the standing wave follows a Bessel Function.

30. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Mutes • The French Horn player’s hand modifies the radiation characteristics of the horn, as well as the effective flare. • Mutes reduce the effective area of the horn and, therefore, reduce the intensity. • Mutes tend to reduce more the first and second harmonic of the pipe than higher frequency harmonics due to their internal modes of oscillation. • Mutes make brass sound “thin and reedy.”

31. Physics 1251 Unit 3 Session 30 The Timbre of Wind Instruments Summary: • The pitch of a wind instrument is determined by the length and shape of its air column. • Feedback from the resonances of the pipe select the frequency of oscillation of the jet, reed or lip-valve. • The excitation, transmission and emittance of the sound in the horn determine the timbre of the instrument.