The Physics
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Opus in profectus

The Nature of Sound

Discussion

introduction

Sound is a longitudinal, mechanical wave.

Sound can travel through any medium, but it cannot travel through a vacuum. There is no sound in outer space.

Sound is a variation in pressure. A region of increased pressure on a sound wave is called a compression (or condensation). A region of decreased pressure on a sound wave is called a rarefaction (or dilation).

The sources of sound

• vibrating solids
• rapid expansion or compression (explosions and implositons)
• Smooth (laminar) air flow around blunt obstacles may result in the formation of vorticies (the plural of vortex) that snap off or shed with a characteristic frequency. This process is called vortex shedding and is another means by which sound waves are formed. This is how a whistle or flute produces sound. Aslo the aeolian harp effect of singing power lines and fluttering venetian blinds.

What are the different characteristics of a wave? What are the things that can be measured about waves? Amplitude, frequency (and period), wavelength, speed, and maybe phase. Deal with each one in that order.

amplitude, intensity, loudness, volume

Amplitude goes with intensity, loudness, or volume. That's the basic idea. The details go in a separate section.

[ISO 226:2003]

• Unlike our ears and hydrophones, fish ears don’t detect sound pressure, which is the compression of molecules. Instead, they perceive something called particle motion, the tiny back-and-forth movements of particles in response to sound waves.

speed of sound

The speed of sound depends upon the type of medium and its state. It is generally affected by two things: elasticity and inertia. This is the Newton-Laplace equation. Laplace added the γ (gamma) correction factor for ideal gases.

solids

 v = √ E ρ
 E = young's modulus ρ = density

fluids

 v = √ K ρ
 K = bulk modulus ρ = density

ideal gases

 v = √ K = √ γP = √ γRT = √ γkT ρ ρ M m
 K = bulk modulus γ = cP/cV (specific heat ratio) P = absolute pressure ρ = density T = absolute temperature R = gas constant M = molar mass k = boltzmann's constant m = molecular mass

Acoustic Thermometry of Ocean Climates (ATOC)

• in water, sounds below 1 kHz travel much farther than higher frequencies
• "shipping noise is loudest in the 30 to 200 Hz range [lowest piano note to middle of cello]"
• "blue and fin wales are the loudest sound in the 17 to 30 Hz range"
• "In pre-industrial times, the low frequency range of 15 to 300 Hz in which most of the baleen whales sing was the quietest part of the sound spectrum, nestled between the subsonic ramblings of earthquakes and the higher pitched rattle of wind, waves and rain." Bob Holmes. "Noises Off." New Scientist. 1 March 1997: 30–33.

echoes

scraps

• As with any wave the speed of sound depends on the medium in which it is propagating.
• Sound generally travels faster in solids and liquids than in gases.
• The speed of sound is faster in materials that have some stiffness like steel and slower in softer materials like rubber.
• Factors Which Affect the Speed of Sound in Air.
• The speed of sound in air is approximately 330 m/s (about 1,200 kph or 700 mph).
• The speed of sound in air is nearly the same for all frequencies and amplitudes.
• It increases with temperature.
• Determining the Distance to a Lightning Bolt: Sound waves take approximately 5 seconds to travel 1 mile. Using this information, it is possible to measure one's distance from a lightning bolt. Begin counting immediately after you see the flash. Every five seconds counted is roughly equivalent to one mile of distance.
Speed of sound in various materials Source: probably an old version of the CRC
solids v (m/s) liquids v (m/s)
aluminum 6420 alcohol, ethyl 1207
beryllium 12,890 alcohol, methyl 1103
brass 4700 mercury 1450
brick 3650 water, distilled 1497
copper 4760 water, sea 1531
cork 500 gases (STP) v (m/s)
glass, crown 5100 air, 000 ℃ 331
glass, flint 3980 air, 020 ℃ 343
glass, pyrex 5640 argon 319
gold 3240 carbon dioxide 259
granite 5950 helium 965
iron 5950 hydrogen (H2) 1284
lucite 2680 nitrogen 334
marble 3810 nitrous oxide 263
rubber, butyl 1830 oxygen (O2) 316
rubber, vulcanized 54 water vapor, 134 ℃ 494
silver 3650 biological materials v (m/s)
steel, mild 5960 soft tissues 1540
steel, stainless 5790
titanium 6070
wood, ash 4670
wood, elm 4120
wood, maple 4110
wood, oak 3850

frequency, pitch, tone

The frequency of a sound wave is called it pitch. High frequency sounds are said to be "high pitched" or just "high"; low frequency sounds are said to be "low pitched" or just "low".

f (THz) device, event, phenomena, process
0.1–2 SASER (sound laser)
f (MHz) device, event, phenomena, process
1–20 medical ultrasound
f (kHz) device, event, phenomena, process
25–80 bat sonar clicks
40–50 ultrasonic cleaning
32.768 quartz timing crystal
18–20 upper limit of human hearing
4–5 field cricket (Teleogryllus oceanicus)
2.2–2.8 clapping
2–5 maximum sensitivity of the human hear
f (Hz) device, event, phenomena, process
300–3000 voice frequency (VF), important for understanding speech
2048 C7 scientific scale, highest note of a soprano singer (approximate)
440 A4 american standard pitch, tv test pattern tone
435 A4 international pitch
426.67 A4 scientific scale
261.63 C4 american standard pitch
258.65 C4 international pitch
256 C4 scientific scale, typical fundamental frequency for female vocal cords
128 C3 scientific scale, typical fundamental frequency for male vocal cords
64 C2 scientific scale, lowest note of a bass singer (approximate)
90 ruby-throated hummingbird in flight
60 alternating current hum (US and Japan)
50 alternating current hum (Europe)
8–20 lower limit of human hearing
17–30 blue and fin wales are the loudest marine sounds in this range
Frequency of Selected Sounds

human hearing and speech

Humans are generally capable of hearing sounds between 20 Hz and 20 kHz (although I can't hear sounds above 13 kHz). Sounds with frequencies above the range of human hearing are called ultrasound. Sounds with frequencies below the range of human hearing are called infrasound.

• Typical sounds produced by human speech have freqeuncies on the order of 100 to 1,000 Hz.
• The peak sensitivity of human hearing is around 4000 Hz.
• locating the source of sound
• Interaural Time Difference (ITD)
• Interaural Phase Difference (IPD) Phase differences are one way we localize sounds. Only effective for wavelengths greater than 2 head diameters (ear-to-ear distances).
• Interaural Level Difference (ILD) Sound waves diffract easily at wavelengths larger than the diameter of the human head (around 500 Hz wavelength equals 69 cm). At higher frequencies the head casts a "shadow". Sounds in one ear will be louder than the other.
• The human ear can distinguish some…
• 1400 different pitches
• three (four?) vocal registers
• (whistle register?)
• falsetto
• modal — the usual speaking register
• vocal fry — the lowest of the three vocal registers

More in the next section.

infrasound

• avalanches: location, depth, duration
• meteors: altitude, direction, type, size, location
• ocean waves: storms at sea, magnitude, spectra
• severe weather: location, intensity
• turbulence: aircraft avoidance, altitude, strength, extent
• earthquakes: precursors, seismic-acoustic coupling
• volcanoes: location, intensity
• Elephants, whales, hippos, rhinoceros, giraffe, okapi, and alligator are just a few examples of animals that create infrasound.
• Some migratory birds are able to hear the infrasonic sounds produced when ocean waves break. This allows them to orient themselves with coastlines.
• An elephant is capable of hearing sound waves well below our the human hearing limitation (approximately 30 Hertz). Typically, an elephant's numerous different rumbles will span between 14 and 35 Hertz. The far reaching use of high pressure infrasound opens the elephant's spatial experience far beyond our limited capabilities.
• Silent Thunder, Katy Payne

ultrasound

• animal echolocation
• microchiropterans a.k.a. microbats: carnivorous bats (not fruit bats or flying foxes)
• cetaceans: dolphins, porpoises, orcas, whales
• two bird species: swiftlets and oilbirds
• some visually impared humans have learned this technique
• sonar (an acronym for sound navigation and ranging) including
• bathymetry
• echo sounding
• fish finders
• medical ultrasonography (the images generated are called sonograms).
Typical parameters used for medical ultrasound Source: Physics Today
frequency
(MHz)
power
(W)
intensity
(W/cm2)
pulse
duration
imaging, echo 1 20 0.05 1.75 0.2 1 μs
imaging, doppler 1 20 0.15 15.7 0.3 10 μs
physiotherapy 0.5 3 < 3 2.5 continuous
surgery 0.5 10 ~ 200 1,500 1 16 s
fish actinopterygii frequency range (Hz)
american shad Alosa sapidissima 200 180,000
goldfish Carassius auratus 5 2,000
atlantic cod Gadus morhua 2 500
tuna Thunnus … 50 1,100
catfish … … 50 4,000
amphibians amphibia frequency range (Hz)
tree frog … … 50 4,000
bullfrog Lithobates catesbeianus 100 2,500
cave salamander Proteus anguinus 10 10,000
reptiles reptilia, sauropsida frequency range (Hz)
red-eared slider Trachemys scripta elegans 68 840
spectacled caiman Caiman crocodilus 20 6,000
birds aves frequency range (Hz)
mallard duck Anus platyrhynchus 300 8,000
pigeon Columba livia ? 5,800
chicken Gallus gallus 125 2,000
canary Serinus canaria 250 8,000
cockatiel Nymphicus hollandicus 250 8,000
parakeet Melopsittacus undulatus 200 8,500
penguin Spheniscus demersus 100 15,000
owl … … 200 12,000
mammals mammalia frequency range (Hz)
cattle Bos taurus 23 35,000
sheep Ovis aries 100 30,000
pig Sus scrofa domestica 45 45,000
dog Canis lupus familiaris 67 45,000
cat Felis silvestris catus 45 64,000
ferret Mustela putorius furo 16 44,000
raccoon Procyon lotor 100 40,000
blue whale Balaenoptera musculus 5 12,000
humpback whale Megaptera novaeangliae 30 28,000
risso's dolphin Grampus griseus 8,000 100,000
beluga whale Delphinapterus leucas 1,000 123,000
atlantic bottlenose dolphin Tursiops truncatus 75 150,000
greater horseshoe bat Rhinolophus ferrumequinum 2,000 110,000
jamaican fruit bat Artibeus jamaicensis 2,800 131,000
northern quoll Dasyurus hallucatus 500 40,000
opossum … … 500 64,000
hedgehog … … 250 45,000
rabbit … … 360 42,000
horse Equus caballus 55 33,500
japanese macaque Macaca fuscata 28 34,500
old world monkeys … … 60 40,000
human Homo sapiens 31 17,600
asian elephant Elephas maximus 16 12,000
guinea pig Cavia porcellus 54 50,000
chinchilla Chinchilla lanigera 90 22,800
hamster Mesocricetus auratus 80 45,000
rat Rattus … 500 64,000
mouse Mus … 2,300 85,500
gerbil Meriones unguiculatus 100 60,000
manatee Trichechus manatus latirostris 400 46,000
insects - insecta frequency range (Hz)
noctuid moth … … 1,000 240,000
grasshopper … … 100 50,000
Frequency Hearing Ranges for Selected Animals (60 dB)