Loudness' We start with pure tones or a pure frequency' - PowerPoint PPT Presentation

1 / 38
About This Presentation
Title:

Loudness' We start with pure tones or a pure frequency'

Description:

The intensity, a physical quantity, is related to to the amplitude square ... Pianoforte family: lute, koto,viguela, cembalo, harpsichord, harp, pianoforte, ... – PowerPoint PPT presentation

Number of Views:61
Avg rating:3.0/5.0
Slides: 39
Provided by: phy87
Category:

less

Transcript and Presenter's Notes

Title: Loudness' We start with pure tones or a pure frequency'


1
Loudness. We start with pure tones or a pure
frequency. The intensity, a physical quantity, is
related to to the amplitude square and for sound
waves, pressure waves, to the variation of
pressure. In fact the precise formula is
I 0.00234 . (?p)2 W/m2 ,
and the pressure expressed in Newtons/m2 The
faintest sound we can perceive at 1000 Hz is
10-12 W/m2 which means a pressure variation of
2.10-5 Newtons/m2 which is 2.10-10 normal
atmospheric pressure! A typical musical
instrument has a typical output, assuming a
spherical wave emission (not really true)
between 0.01 Watt for a clarinet to 6.4 W for a
trombon playing fortissimo. This is the output in
all directions. Given a tone of a given
frequency there are two important concepts
the threshold of hearing or lowest audible
intensity and the upper limit of hearing beyond
which one feels pain.
2
Instruments by family
Pianoforte family lute, koto,viguela, cembalo,
harpsichord, harp, pianoforte, modern electronic
versions of some of these Violin family violin,
viola, cello, counterbass Woodwind
familyclarinet, oboe, basson, flute, recorder
(in many forms) harmonica Brass
instrumentsclarinet, oboe, basson, horn,
saxophon, shofar Percussion triangle, celesta,
drums, cymbal, bells, Organ on a class if its
own Electronic many of the above plus ondes
Marthenot Voice a reed instrument classified as
its own class
3
instrument family
4
Plucked instruments
5
Plucking mechanism for harpsichord
6
Radiated spectrum of harpsichord
7
Harp mechanism
8
Guitar radiation zones
9
Guitar structure
10
Guitar vibration modes
11
Vibrations when bracing is introduced
12
Modes of the complete system
13
waveforms
14
Frequencies of different elements
15
Time and frequency analysis
16
More on time
17
Piano generalities
  • f 1/2LvF/µ
  • This contains the three Mersenne laws
  • Frequency is inversely proportional to length.
  • Frequency is inversely proportional to mass
    density per unit length (µ)
  • The frequency is proportional to the tension.
  • These considerations determine how the modern
    piano is built
  • 243 strings varying in length from 2m to 5 cm.
  • 8 are wrapped in a single wire envelope, 5 pairs
    also wrapped ,
  • 7 made of 3 wrapped strings and 68 of a r
    unwrapped ones.
  • This makes a total of 88 notes or a bit more of
    seven octaves.

18
Piano history
19
Piano history 2
20
Piano history 3
21
Piano history 4
22
Piano action
23
Science helps striking
24
Details of hammer striking
25
Subtleties in hammer structure
26
Piano touch and sound dependence
  • The piano is the upmost example of an instrument
    related to a given music period. The relation of
    the player to the instrument is strong.
  • However, is the touch relevant? Pianists pay
    attention to the way the notes are pressed but in
    fact as we will soon see amplitude and frequency
    depend only on the velocity of the hammer. The
    loudness and the timbre are intimately linked
    because the strength of the hit determines the
    excitation of the harmonics. As usual there is
    more to it since there are nonlinear effects due
    to the deformation and inelasticity of the felt.
    In short, hitting harder does increase the power
    but also increases the proportion of higher
    harmonics and therefore
  • The timbre is more brilliant.

27
Piano spectra as a function of hammer hardness
28
Diagram of a piano
29
Piano resonance cavity modes
30
Piano inharmonicity
31
String and hammer inharmonicity
String inharmonicity and hammer effects
The hammer gets deformed striking the chord and
it is not anymore a point contact, this
introduces inharmonicity. The string reflects
waves to the hammer and these in turn combine to
produce an effect. The string should be as tight
for power reasons see below and as thin as
possible to avoid inharmonicities. In fact
with B0.004
The inharmonicity at the 17th partial is 1
which is quite audible.
B p2ESK2/TL2
Where E is Young modulus, T the tension, S the
area, K the radius of giration
32
Decay time
33
inharmonicity
34
Position of the notes
35
Parallel and perpendicular vibration decay
36
Tuning and inharmonicity
37
Radiated power and position of source
38
Piano radiation pattern
Write a Comment
User Comments (0)
About PowerShow.com