PHY2464 - The Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 16
16
Reed
Reed Instruments
Instruments
Adapted
Adapted from
from Sam
Sam Matteson’s
Matteson’s
Unit
Unit 33 Sessions
Sessions 28
28
Sam
Sam Trickey
Trickey
Mar.
Mar. 2,
2, 2005
2005
PHYPHY-2464
Pres. 16 Reed Instruments
Reed instruments:
• Thin, elastic, vibrating “flap” at one end of a
pipe
• Flap made of natural reed is origin of the name.
• KEY FACT –
Pipe is closed at reed end to excellent approximation
•There are single-reed and double-reed instruments
Single reeds: clarinets, saxophones, organ reed pipes…
Double reeds: oboe, bassoon, english horn, krummhorn
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 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
~
PHYPHY-2464
♩♪♫
f1 f2 f3 f4
~
Pres. 16 Reed Instruments
Bicycle Horn
Reed
fn
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
The Clarinet:
Bell
Body
Reed
The clarinet body has a cylindrical
bore.
PHYPHY-2464
Pres. 16 Reed Instruments
Reminder: Bernoulli Effect
•
The pressure at a place in a fluid decreases as the
velocity increases at that place.
Thus, as the air flows past a reed bent open, it
is forced closed.
Bernoulli Effect
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
The Single Reed
Key FACT: 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
Tonguing
PHYPHY-2464
Reed
Pres. 16 Reed Instruments
Hard and Soft Reeds
A hard reed is one for which the favored vibration
frequency is determined by the reed stiffness and
dimensions.
A soft reed flexes easily and vibrates at the
frequency of external pressure fluctuations.
Soft Reeds
Hard Reed:
Harmonica
Clarinet
Oboe
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
Harmonium or Reed Organ
Hard or soft reed?
PHYPHY-2464
Pres. 16 Reed Instruments
Double Reed
Bassoons
use a double
reed, as do
Oboes, English
Horns, and
Krummhorns
Bassoon Reeds
Reed
Double
Reed
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
The Double Reed
The reed opens and closes like a valve, pressurizing
the pipe when open, closing due to the Bernoulli
effect when the air flows.
Pressure Pulses
Air flow
Reed Tip
PHYPHY-2464
Pres. 16 Reed Instruments
Key INSIGHT: feedback from the pressure standing wave
locks the frequency of the oscillation of the reed.
Notice stopped cylindrical pipe → only odd harmonics
Pressure wave
f2n(2n-1) v/ 4L′
2n-1 = (2nL′ = L + 0.6 r
Pressure inverts
0.6 r
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
Other Bore Shapes:
Conical Pressure
antianti-node
PHYPHY-2464
Pressure
node
Pressure
antianti-node
Pres. 16 Reed Instruments
Key FACT - For a stopped conical pipe
fn ≈ n v / 2(L′ + c)
if c << λ
L′ = L + 0.6 r
L′
c
d=2r
0.6 r
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
Why?
Z ( = acoustic impedance) changes along
the length of the pipe.
Reminder: Z goes as 1/S
Weighted String Analogy
PHYPHY-2464
Pres. 16 Reed Instruments
Other Reed Woodwinds:
English horn:
Conical bore
Saxophone: Conical bore
Oboe: Conical bore
Bassoon:
Conical bore
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
The Reed Pipes of Organs:
•
•
•
Often
Conical
Pipe
Shallot
Voiced
by Reeds
Reed
Tuned by
Spring
Tuning
Spring
PHYPHY-2464
Pres. 16 Reed Instruments
Reed Pipes
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
To see more on reed pipes click on
“The Organ and How It Works”→ “Pipes”
→“Reed Pipe Construction”
jhcook//OrgHist/begin.
htm
at http://panther.bsc
http://panther.bsc..edu/~
edu/~jhcook
OrgHist/begin.htm
The immense variety of organ pipes is evident from
browsing the drawings at
http://www.organstops
.org/_apps/Illustrations.html
http://www.organstops.org/_apps/Illustrations.html
For examples of three different organ reed resonator
forms, compare capped oboe, musette, and french
horn
PHYPHY-2464
Pres. 16 Reed Instruments
Edge versus Reed
Cylindrical vs. Conical
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 16 Reed Instruments
Summary
• 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.
• Organ reed pipe resonators have many forms,
often conical or modfied conical