MUSIC 150 MUSICAL ACOUSTICS
BRASS
INSTRUMENTS
REFERENCE: CHAPTER 11 IN SCIENCE OF SOUND
CHAPTER 14 IN THE PHYSICS OF MUSICAL
INSTRUMENTS
SOME BRASS INSTRUMENTS
PLAYING
RANGES
COMPARISON OF BRASS INSTRUMENTS
RESONANCES
OF OPEN AND
CLOSED PIPES
OSCILLATIONS IN A PIPE
THE AIR COLUMN OF A Bb TRUMPET HAS A LENGTH
OF ABOUT 140 cm. THE RESONANCES OF A CLOSED
PIPE OF THIS LENGTH SHOULD OCCUR AT:
fn = nc/4L = 343 n/4(1.4) = 61.3 n (n = 1 , 3, 5, 7, . . .)
= 61, 184, 306, 429 . . . Hz
ONE WAY TO STUDY THE RESONANCES OF A PIPE
(OR A WIND INSTRUMENT) IS TO MAKE A GRAPH OF
ITS ACOUSTIC IMPEDANCE AS A FUNCTION OF
FREQUENCY
ACOUSTIC IMPEDANCE IS SOUND PRESSURE
DIVIDED BY VOLUME VELOCITY Z = p/U
APPARATUS FOR
GRAPHING THE
ACOUSTIC
IMPEDANCE OF
WIND
INSTRUMENTS
FEEDBACK
INPUT VALVES
REED-GENERATOR
CONFIGURATIONS
(a) Corresponds to a
woodwind reed
(b) Corresponds to brass
player’s lips
(c) Alternative model of
brass player’s lips
BENADE’S “WATER TRUMPET”
(INPUT VALVE IS CONTROLLED BY PRESSURE FEEDBACK)
MOUTHPIECE
THE BELL:
CHANGES THE FREQUENCIES AND
HEIGHTS OF THE IMPEDANCE PEAKS
CHANGES THE RADIATION PATTERN
(More directional)
CHANGES THE SPECTRUM OF THE
RADIATED SOUND
ALLOWS MORE EFFICIENT SOUND
RADIATION (MATCHES IMPEDANCES)
IMPEDANCES
COMPARED TO A
MUSICAL SCALE
REFLECTION POINT IN THE BELL
THE TURNING POINT MOVES OUTWARD IN THE BELL AS THE
FREQUENCY INCREASES MODE FREQUENCIES ARE NEARLY
IN THE RATIOS 0.8 : 2 : 3 : 4
BERNOULLI EFFECT
REDUCED
PRESSURE IN THE
CENTER SECTION
CAUSES THE
LIQUID IN THE UTUBE TO STAND AT
A HIGHER LEVEL
REDUCED
PRESSURE IN AIR
JET FROM A
VACUUM CLEANER
HOSE GIVES RISE
TO A NET UPWARD
FORCE FB
BLOWING DOWNWARD
THROUGH THE SPOOL
CAUSES AIR TO FLOW
OUTWARD,
SUPPORTING A CARD
AND PIN BY MEANS OF
THE BERNOULLI FORCE
SLIDES AND VALVES
PLAYING POSITIONS OF A TROMBONE SLIDE
PRESSING DOWN ON
TRUMPET VALVE
LENGTHENS THE
THE TRUMPET
TUBING
IMPEDANCE CURVES FOR TWO TROMBONES
HAND IN A FRENCH HORN BELL
PRESSURE INSIDE AND OUTSIDE A TRUMPET
SHOCK WAVES IN BRASS
INSTRUMENTS
ONLY A SMALL PART OF THE SOUND ENERGY
THAT REACHES THE BELL IS RADIATED; THE
REST IS REFLECTED
SOUND LEVELS AS HIGH AS 175 dB INSIDE A
TRUMPET
NONLINEAR EFFECTS CREATE SHOCK WAVES
TRANSIENTS
TRANSIENTS ARE IMPORTANT IN IDENTIFYING
MUSICAL INSTRUMENTS (see Section 7.11)
BELOW CUTOFF: FEEDBACK STABILIZES
OSCILLATION
ABOVE CUTOFF: PARTIALS BUILD UP SLOWLY
WITHOUT STRONG FEEDBACK
LIPS ARE MORE OR LESS “ON THEIR OWN” UNTIL THE
FIRST REFLECTED WAVE COMES BACK
TO ATTACK A NOTE CORRECTLY REQUIRES TRAINED
LIPS (ESPECIALLY ON A FRENCH HORN)
MUTES
MUTES
VIBRATIONS OF A TROMBONE BELL
PERFORMANCE
OBSERVING THE LIPS THROUGH A GLASS
MOUTHPIECE WINDOW