Sound

Production of sound

• Sound is produced by vibrations in a medium.
• Sound can not be produced in a vacuum, nor can sound travel across a vacuum.
• Vibrations whose frequency is too low to hear is called infrasound.
• Vibrations whose frequency is too high to hear is called ultrasound.
• Vibrations produce pressure waves that oscilate parallel to the direction of propagation.
• Sound is a longitudinal wave.

Relative speed of sound in solids, liquids and gases

• Speed of sound in solids > liquids > gases.
  • The reason why sound travels the fastest in solids is because solids are the most stiff.
• With all else being equal...
  • Speed of sound in stiff objects > compressible objects.
  • Speed of sound in less dense objects > more dense objects. Even though gases are less dense than solids, sound still travels slower in them because they are too compressible.
  • Speed of sound in hot objects > cold objects.

Intensity of sound (decibel units, log scale)

• β = 10 log^I/_I0
• β is sound level in decibels. I is intensity. I₀ is 10^-12 W/m²
• Intensity is power per area, or the rate of energy expenditure per area. The unit is W/m²
• 

• Intensity	Decibels
  I0	0
  10 I0	10
  100 I0	20
  1000 I0	30

• The decibel system is based on human perception. The decibel value for sound with an intensity of I₀ is zero - below this intensity, sound is not audible. As intensity increases, our perception of its loudness only increases to a much lesser degree.

Attenuation

• Sound attenuation is the gradual loss of intensity as sound travels through a medium.
• Sound attenuation is the greatest for soft, elastic, viscous, less dense material.

Doppler effect (moving sound source or observer, reflection of sound from a moving object)

• Situations where the observed frequency is higher than the actual:
  • Source moving toward stationary observer: f_o = f_s ^v/_{v - vs}
  • Observer moving toward stationary source: f_o = f_s ^{v + v_o}/_v
  • Source and observer both moving toward each other: f_o = f_s ^{v + v_o}/_{v - vs}
• Situations where the observed frequency is lower than the actual:
  • Source moving away from stationary observer: f_o = f_s ^v/_{v + vs}
  • Observer moving away from stationary source: f_o = f_s ^{v - v_o}/_v
  • Source and observer both moving away from each other: f_o = f_s ^{v - v_o}/_{v + vs}
• Situations where the observed frequency could be either higher or lower than the actual:
  • Source moving toward the observer, but the observer is moving away from the source: f_o = f_s ^{v - v_o}/_{v - vs}
  • Source moving away from observer, but the observer is moving toward the source: f_o = f_s ^{v + v_o}/_{v + vs}
• f_o is observed frequency. f_s is actual frequency emitted by the source. v is the speed of sound. v_o is the speed at which the observer is travelling. v_s is the speed at which the source is travelling.

Pitch

• Pitch is the human perception of the frequency of sound.
• Higher frequency = higher pitch.

Resonance in pipes and strings

• 
• Frequencies can be obtained by f = v/λ
• Both strings and pipes open at both ends have L = ⁿ/₂λ
• Pipes with a closed end have L = ^(2n-1)/₄λ

Harmonics

• The fundamental frequency is called the first harmonic (n = 1).
• The next-up frequency is called the second harmonic (n = 2).

Ultrasound

• Sound has 3 fundamental properties: reflection, refraction, and diffraction.
• Ultrasound imaging is based on the reflection property of sound.
• A source emits ultrasound, which reflects off a surface back into the detector to form an image.
• Ultrasound is sound that is too high in frequency for humans to hear.