Dr' James van Howe

1
PH 105
Resonance in Musical Instruments and Fourier
Synthesis
Dr. James van Howe Lecture 8
Interferograms of different resonant modes on the
violin
2
Who is the singer?

• Leonard Cohen
• Jeff Buckley
• Rufus Wainwright
• Alexandra Burke

3
What is the most important in order to get the
child to swing the highest?

• Making sure to push hard
• Making sure to push at the right time
• Making sure the length of swing is right
• Making sure the child is not too heavy

4
True or False
Most of the sound energy generated by a violin or
guitar comes from vibration of the strings
5
Resonance in Tubes
Which picture accurately shows the standing waves
for the fundamental mode in a Open-Open tube?
A
C
B
D
6
Resonance in Tubes
Which picture accurately shows the displacement
antinodes for the fundamental mode in a closed
tube?
A
C
B
D
7
What is the spectrum if I play both sine waves at
the same time?
Spectrum
A.
1
0.8
0.6
Amplitude
0.4

0.2
0
440
880
Frequency (Hz)
B.
1
0.8
0.6
Amplitude

0.4
0.2
0
440
880
Frequency (Hz)
8
Finish Activity Strings and Tubes
9
Definitions

• Harmonic whole number multiples of the
  fundamental frequency
• Overtones multiples of the fundamental that are
  not necessarily whole number
• Partials all overtones
• Octave interval between two tones that is a
  ratio of 21

10
Resonance in Musical Instruments

• String Instruments modes on a string
• Percussion string-like modes, i.e. drum
  two-dimensional string
• Brass, woodwinds, human voice modes in open and
  closed tubes
• Helmholtz resonator (sound box) cavity modes

11
Chladni Patterns
12
Helmholtz Resonator Cavity
Cross sectional area of neck, A
m mass of air in neck

k springiness of air in cavity
Volume of Air, V
Resonant frequency
What needs to happen to the volume of air to get
a higher pitch? Think about blowing across a pop
bottle that is empty and one that is half full
(less air).
13
Examples of Helmholtz Resonators

• Late 19th century spectrum analyzer way to
  select and listen to (measure) one frequency
• Air resonance of a guitar or violin sound box
• Reflex port of loudspeaker cabinet neck into
  cabinet allows air resonance
• Automobile mufflers side branch absorbs sound

14
Sympathetic Vibration
Demo tuning fork

• Violin, piano, or guitar strings make very little
  sound
• By connecting the strings to the top plate
  through the bridge, the vibrations are
  transmitted to the plate and soundboard
• Top plate has a much bigger surface area and move
  a much larger volume of air (can think of the
  plate as many little strips or strings vibrating
  constructively) amplifying the sound

15
True or False
Most of the sound energy generated by a violin or
guitar comes from vibration of the strings
16
Resonance in Tubes
Which picture accurately shows the standing waves
for the fundamental mode in a Open-Open tube?
A
C
B
D
17
Resonance in Tubes
Which picture accurately shows the displacement
antinodes for the fundamental mode in a closed
tube?
A
C
B
D
18
What is the spectrum if I play both sine waves at
the same time?
Spectrum
A.
1
0.8
0.6
Amplitude
0.4

0.2
0
440
880
Frequency (Hz)
B.
1
0.8
0.6
Amplitude

0.4
0.2
0
440
880
Frequency (Hz)