The Physics
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# 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).

Magnify

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)…

#### 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
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".

Frequency of selected sounds
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
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
• 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
Typical parameters used in 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