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 implosions)
- Smooth (laminar) air flow around blunt obstacles may result in the formation of vortices (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. Also 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. Sound generally travels faster in solids than in liquids than in gases.
The speed of sound in a medium 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.
For solids…
| v = √ | E |
| ρ |
| E = | Young's modulus |
| ρ = | density |
For fluids (which incudes liquids and gases)…
v = √ |
K |
ρ |
| K = | bulk modulus |
| ρ = | density |
For 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 constant |
| m = | molecular mass |
solids
Hi there. The speed of sound is faster in solids that have some stiffness like steel and slower in those that are softer like rubber.
fluids
Basically liquids. Actually, basically water.
The speed of sound in water is somewhat difficult to determine since it is affected by temperature, pressure, density, and salinity (or the amount of any other other dissolved substances). The speed of sound in water can be found using this emprically derived equation…
v = 1449.2 + 4.6 T − 0.055 T2 + 0.00029 T3 + (1.34 − 0.010 T)(s − 35) + 0.16 h
where…
| T = | temperature in ˚C (0 T ≤ 35 °C) |
| s = | salinity in parts per thousand (0 ≤ s ≤ 45 ppt, but usually 35 ± 2 ppt) |
| h = | depth in meters (0 ≤ h ≤ 1000 m) |
Generally, an increase in temperature and salinity will increase the speed of sound in water. Usually, ocean salinity is estimated at around 35 ppt, so the equation above is essentialy a function of temperature and depth.
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.
ideal gases
Let's be honest. All we really care about is the speed of sound in air.
- The speed of sound in air is approximately 345 m/s (about 1250 kph, 770 mph, 1100 ft/s).
- The speed of sound in air is nearly the same for all frequencies and amplitudes.
- It increases with temperature.
The speed of sound in air as a function of temperature can be found using these approximate equations…
- the linear one
- the one with the square root in it
echoes
Where should this go?
Speed of sound in various materials
| solids | v (m/s) |
|---|---|
| aluminum | 6,420 |
| beryllium | 12,890 |
| brass | 4,700 |
| brick | 3,650 |
| copper | 4,760 |
| cork | 500 |
| glass, crown | 5,100 |
| glass, flint | 3,980 |
| glass, pyrex | 5,640 |
| gold | 3,240 |
| granite | 5,950 |
| iron | 5,950 |
| lead | 2,160 |
| lucite | 2,680 |
| marble | 3,810 |
| rubber, butyl | 1,830 |
| rubber, vulcanized | 54 |
| silver | 3,650 |
| steel, mild | 5,960 |
| steel, stainless | 5,790 |
| titanium | 6,070 |
| wood, ash | 4,670 |
| wood, elm | 4,120 |
| wood, maple | 4,110 |
| wood, oak | 3,850 |
| liquids | v (m/s) |
|---|---|
| alcohol, ethyl | 1,207 |
| alcohol, methyl | 1,103 |
| mercury | 1,450 |
| water, distilled | 1,497 |
| water, sea | 1,531 |
| gases (STP) | v (m/s) |
| air, 000 °C | 331 |
| air, 020 °C | 343 |
| argon | 319 |
| carbon dioxide | 259 |
| helium | 965 |
| hydrogen (H2) | 1,284 |
| neon | 435 |
| nitrogen | 334 |
| nitrous oxide | 263 |
| oxygen (O2) | 316 |
| water vapor, 134 °C | 494 |
| biological materials | v (m/s) |
| soft tissues | 1,540 |
Source: probably an old version of the CRC
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 (Hz) | device, event, phenomenon, process |
|---|---|
| 0.1–2.0 × 1012 | SASER (sound laser) |
| 01–20 × 106 | medical ultrasound |
| 25–80 × 103 | bat sonar clicks |
| 40–50 × 103 | ultrasonic cleaning |
| 32.768 × 103 | C11 scientific scale (215 Hz), quartz timing crystal |
| 18–20 × 103 | upper limit of human hearing |
| 4–5 × 103 | field cricket (Teleogryllus oceanicus) |
| 2.2–2.8 × 103 | clapping |
| 2–5 × 103 | maximum sensitivity of the human hear |
| 4,186 | C8 highest note on a modern piano |
| 0,300–3,000 | voice frequency (VF), important for understanding speech |
| 2,048 | C7 scientific scale, highest note of a soprano singer |
| 440 | A4 standard tuning frequency (ISO 16), TV test pattern tone |
| 435 | A4 international pitch (diapason normal) |
| 422 | A4 classical pitch |
| 256 | C4 scientific scale (28 Hz), typical fundamental frequency for female vocal cords |
| 128 | C3 scientific scale (27 Hz), typical fundamental frequency for male vocal cords |
| 64 | C2 scientific scale (26 Hz), lowest note of a bass singer |
| 90 | ruby-throated hummingbird in flight |
| 60 | alternating current hum (US and Japan) |
| 50 | alternating current hum (Europe) |
| 27.5 | A0 lowest note on a modern piano |
| 17–30 | blue and fin wales are the loudest marine sounds in this range |
| 08–20 | lower limit of human hearing |
| 1–5 | tornadoes |
| 2 | C−3 scientific scale (21 Hz) |
| 1 | C−4 scientific scale (20 Hz) |
| 3 × 10−15 | B♭−53, lowest note in the universe (a black hole in the Perseus cluster of galaxies) |
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 frequencies on the order of 100 to 1,000 Hz.
- The peak sensitivity of human hearing is around 4,000 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…
- 1,400 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
- tornadoes: detection, location, warning, core radius, funnel shape, precursors
- 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 impaired 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).
Frequency hearing ranges for selected animals (60 dB, *except)
| fish | – | actinopterygii | frequency range (Hz) | ||
|---|---|---|---|---|---|
| American shad | – | Alosa sapidissima | 200 | – | 180,0001 |
| goldfish | – | Carassius auratus | 20 | – | 4,0002 |
| " | 70 | – | 4,6003 | ||
| " | 200 | – | 4,0004 | ||
| Atlantic cod | – | Gadus morhua | 30 | – | 4705 |
| " | 18 | – | 4006 | ||
| yellowfin tuna | – | Thunnus albacares | 200 | – | 8007 |
| " | 200 | – | 8008 | ||
| cutthroat trout | – | Oncorhynchus clarkii | 50 | – | 4439 |
| Raphael catfish | – | Platydoras costatus | 200 | – | 4,0004 |
| amphibians | – | amphibia | frequency range (Hz) | ||
| American green tree frog | – | Dryophytes cinereus | 100 | – | 5,00010 |
| American bullfrog | – | Lithobates catesbeianus | 100 | – | 3,20010 |
| " | 100 | – | 2,5002 | ||
| (olm) cave salamander | – | Proteus anguinus | 10 | – | 10,00011 |
| reptiles | – | reptilia | frequency range (Hz) | ||
| spectacled caiman | – | Caiman crocodilus | 20 | – | 6,00012 |
| green sea turtle | – | Chelonia mydas | 100 | – | 5008 |
| red-eared slider | – | Trachemys scripta elegans | 68 | – | 8402 |
| birds | – | aves | frequency range (Hz) | ||
| mallard duck | – | Anas platyrhynchus | 66 | – | 7,60013 |
| pigeon | – | Columba livia | ? | – | 5,8002 |
| chicken | – | Gallus domesticus | 9 | – | 7,20014 |
| canary | – | Serinus canaria | 250 | – | 9,00015 |
| cockatiel | – | Nymphicus hollandicus | 250 | – | 8,00016 |
| budgerigar | – | Melopsittacus undulatus | 40 | – | 14,00017 |
| African penguin | – | Spheniscus demersus | 100 | – | 15,00018 |
| great horned owl | – | Bubo virginianus | 60 | – | 7,00019 |
| mammals | – | mammalia | frequency range (Hz) | ||
| cattle | – | Bos taurus | 23 | – | 35,00020 |
| goat | – | Capra hircus | 78 | – | 37,00021 |
| sheep | – | Ovis aries | 100 | – | 40,00022 |
| pig | – | Sus domesticus | 42 | – | 40,50021 |
| whitetail deer | – | Odocoileus virginianus | 115 | – | 54,00023 |
| horse | – | Equus caballus | 55 | – | 33,50020 |
| dog | – | Canis familiaris | 67 | – | 45,00024 |
| cat | – | Felis catus | 48 | – | 85,00025 |
| ferret | – | Mustela putorius furo | 36 | – | 44,00026 |
| raccoon | – | Procyon lotor | 100 | – | 40,00027 |
| blue whale | – | Balaenoptera musculus | 5 | – | 12,00028 |
| fin whale | – | Balaenoptera physalus | 5 | – | 12,00028 |
| humpback whale | – | Megaptera novaeangliae | 50 | – | 12,00028 |
| Risso's dolphin | – | Grampus griseus | 8,000 | – | 100,00029 |
| orca | – | Orcinus orca | 600 | – | 114,00030 |
| beluga whale | – | Delphinapterus leucas | 1,400 | – | 108,00031 |
| Atlantic bottlenose dolphin | – | Tursiops truncatus | 75 | – | 150,00032 |
| greater horseshoe bat | – | Rhinolophus ferrumequinum | 2,000 | – | 110,00033 |
| Jamaican fruit bat | – | Artibeus jamaicensis | 2,800 | – | 131,00034 |
| Japanese macaque | – | Macaca fuscata | 28 | – | 34,5002 |
| old world monkeys | – | Cercopithecidae | 60 | – | 40,00035 |
| human | – | Homo sapiens | 31 | – | 17,6002 |
| Philippine tarsier | – | Tarsius syrichta | ? | – | 91,00036 |
| Asian elephant | – | Elephas maximus | 17 | – | 10,50037 |
| guinea pig | – | Cavia porcellus | 86 | – | 46,50038 |
| chinchilla | – | Chinchilla lanigera | 50 | – | 33,00039 |
| hamster | – | Mesocricetus auratus | 80 | – | 45,0002 |
| hispid cotton rat | – | Sigmodon hispidus | 1,000 | – | 72,00040 |
| Merriam's kangaroo rat | – | Dipodomys merriami | 42 | – | 52,00040 |
| Mongolian gerbil | – | Meriones unguiculatus | 100 | – | 60,00041 |
| house mouse | – | Mus musculus | 2,300 | – | 92,00040 |
| " | 2,300 | – | 85,5002 | ||
| laboratory rat | – | Rattus norvegicus domestica | 250 | – | 76,00042 |
| white-tailed prairie dog | – | Cynomys leucurus | 44 | – | 26,00043 |
| black-tailed prairie dog | – | Cynomys ludovicianus | 29 | – | 26,00043 |
| long-eared hedgehog | – | Hemiechinus auritus | 250 | – | 45,00044 |
| domestic rabbit | – | Oryctolagus cuniculus | 96 | – | 49,00040 |
| tree shrew | – | Tupaia glis | 250 | – | 60,00045 |
| northern quoll | – | Dasyurus hallucatus | 500 | – | 40,00046 |
| Virginia opossum | – | Didelphis virginiana | 500 | – | 60,00047 |
| Florida manatee | – | Trichechus manatus latirostris | 400 | – | 46,00048 |
| " | 400 | – | 46,00049 | ||
| " | 250 | – | 90,50050 | ||
| insects | – | insecta | frequency range (Hz) | ||
| owlet moth* | – | Spodoptera eridania | ? | – | 240,00051 |
| greater wax moth* | – | Galleria mellonella | ? | – | 300,00052 |
| mollusks | – | mollusca | frequency range (Hz) | ||
| Pacific oyster* | – | Magallana gigas | 10 | – | 1,00053 |
| 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 |