Contents

1 The sound waves

• Sound waves¹ are sound mechanical waves of pressure that transmit energy through the collision of particles.²
• Sound waves are longitudinal waves³ and velocity of propagation is proportional to the elasticity (or ease of deformation) of the medium.

  Medio	Velocidad
  Air (0o C)	331 m/s
  Air (20o C)	334 m/s
  Oxygen (0o C)	316 m/s
  Hydrogen (0o C)	1.284 m/s
  Lead (20o C)	1.230 m/s
  Watter (15o C)	1.450 m/s
  Iron (20o C)	5.130 m/s
  Granite	6.000 m/s

2 Temporal representation of sound

• Sound waves can be represented by measuring the particles displacement from its equilibrium over time. The result is a graph of the type:

  

3 Frequency representation of sound

• Because the periodic nature of the sound waves, we can also represent the basis of the frequency components⁴ that compose them. This is done using the  color red Fourier Analysis. The result is a graph of the type:

  

4 Frequency analysis of musical notes

• Musical notes are produced by vibrating elements to certain frequencies. By definition, the spectrum of a musical note only has energy (different from zero) in the frequencies:

  where x is the fundamental frequency of the note (which indicates which note is) and 2x,3x, is the pitch of the note (which amplitudes depend on the musical instrument that has produced the notes).

5 A classification of the sound waves

• The most common form of ranking is related to the oscillation frequency. So we can talk about:
  1. Infrasounds: those oscillations with a frequency less than 20 Hz (not perceptible by humans).
  2. Audible Sounds: between 20 and 20.000 Hz.
  3. Ultrasounds: over 20.000 Hz. Also unnoticeable.
• These frequency ranges vary between individuals. These values are average values.

6 Intensity of sound waves

• Sound intensity is dependent on the amplitude of the particle oscillations. These oscillations cause pressure variations in the eardrum. This way we perceive sound.
• The most common way to express a sound intensity I is relatively respect to the intensity needed to reach the threshold of hearing, which by definition is 20μ P of pressure⁵  [?]. In this case, the relative loudness or relative SPL (Sound Pressure Level) is expressed as:

• The human auditory system reacts logarithmically to sound intensity. Therefore, we generally express this physical measure in decibels (dB). In this case:

• The following table shows some examples with typical sound intensities expressed in dB’s. Also it has been added a column to get an idea of the absolute measure of the real intensity I.

  Context	SPL[dB]	I
  Auditory Threshold	0 dB	20μ Pa
  Whisper	20 dB	10 × 20μ Pa
  Conversation	40 dB	100 × 20μ Pa
  Traffic	60 dB	1.000 × 20μ Pa
  Subway	80 dB	10.000 × 20μ Pa
  Threshold of Pain	140 dB	107 × 20μ Pa
  Jet Engine	160 dB	108 × 20μ Pa

• The human ear is able to work properly between 20μ Pa (0 dB) and 100μ Pa (114 dB), approximately [1].

References