The nature and properties of sound

1
The nature and properties of sound

• Jakob Christensen-Dalsgaard,
• Center for Sound Communication, SDU Odense
  University

2
Definition of sound

• Sound is a longitudinal wave propagating in an
  elastic medium
• The sound wave is pressure /medium motion
  oscillations
• Pressure and particle velocity are in phase in
  the propagating sound wave

3
Properties of the sound wave 1

• Some definitions
• Frequency the number of wave cycles/second (f).
• Angular frequency (?) ?2?f
• Wavelength The distance (in m) between two wave
  maxima
• Phase time offset of wave zero crossing compared
  to reference

4
Properties of the sound wave 2

• In the simplest case (tuning fork), the sound is
  generated by a pure sine oscillation and given by
  the expression
• Here, f is the frequency and ? is the phase. P0
  is the sound pressure amplitude

5
Properties of the sound wave 3

• The relationship between frequency (f),
  wavelength (?) and sound velocity (c)
• The sound velocity in air is 340 m/s. For a 1 kHz
  tone this means that the wavelength is 34 cm. In
  water, where the sound velocity is approximately
  1500 m/s, the wavelength for a 1 kHz tone is 1.5 m

6
Properties of the sound wave 4

• Sound pressure and particle velocity During
  sound propagation, the acoustic particles
  oscillate around a rest position.
• Far away from the sound emitter, the particle
  oscillation velocity of the sine tone is given by
• Here, particle velocity oscillations is in phase
  with pressure oscillations.

7
Pressure, velocity, impedance

• The relationship between pressure p and particle
  velocity v in the far-field sound wave is given
  by
• Z is the characteristic impedance of the medium,
  , where c is sound
  velocity in the medium
• and ? is the density

8
Sound intensity

• The sound intensity I, the energy flux radiated
  by the far-field sound wave through a unit area,
  is given by

9
The dB scale

• Sound pressure is usually stated in dB relative
  to a reference pressure
• The most common reference pressure (in air) is 20
  ?Pa (dB SPL), close to the human threshold of
  hearing at 1 kHz
• When sound intensities are used, dB values are
  calculated as
• since I?p2

10
Some useful dB values

• Doubling of sound pressure
• Tenfold increase in sound pressure

11
dB values

• Note that because the dB scale is logarithmic,
  addition means multiplication of the sound
  pressures!
• For example Two sound sources both emit sound in
  phase at 50 dB SPL. What is the resulting sound
  pressure?

12
The distance law

• The area that sound is radiated through increases
  with the square of distance, therefore sound
  intensity drops with the square of distance
• Since intensity is proportional to pressure
  squared, this means that pressure drops with
  distance (usually stated as -6 dB per distance
  doubled)

13
Sound diffraction and reflection

• Objects interact with the sound wave in the
  following ways
• Objects that are smaller than 1/6th wavelength
  are transparent to sound
• Objects with sizes comparable to the wavelength
  scatter or diffract the sound wave
• Objects with sizes more than 5-10 wavelengths
  reflect the sound wave

14
Exercise

• Suppose that a new frog species echolocated at
  500 Hz. What would the minimal sizes of objects
  it could detect (approximately)?

15
Sound reflection

• Sound reflection depends on the difference
  between the characteristic impedance of the
  medium on both sides of the boundary.
• Large impedance differenceslarge fraction of
  sound energy is reflected, small fraction is
  transmitted

16
Reflection

• Reflection from a soft-hard boundary
• Reflection from a hard-soft boundary

17
Temperature and wind effects

• Since sound velocity depends on temperature,
• c331 0.6 T in air
• temperature gradients result in a velocity
  gradient.
• A velocity gradient produces refraction of the
  sound wave according to Snells law

18
Temperature and velocity gradients

• An upward oriented velocity gradient (lower
  ground temperatures) produces downward
  deflection
• A downward oriented gradient (higher ground
  temperatures) produces upward deflection

19
Wind effects, attenuation

• The effect of wind currents is to bend the sound
  wave
• In addition to the drop of sound pressure due to
  spreading, sound can be absorbed/scattered by the
  medium
• Especially humidity effects on ultrasound

20
Doppler shift

• A moving sound source
• compress the sound waves in front of the object
  in the motion direction
• -Increased frequency
• Rarify the sound waves behind the object
• -Decreased frequency

21
Some useful webpages

• Dan Russells acoustics animation page
• http//www.kettering.edu/drussell/Demos.html
• An acoustics tutorial by David Worall at
• http//online.anu.edu.au/ITA/ACAT/drw/PPofM/INDEX.
  html