The Nature of Sound

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© 1998-2008 by Glenn Elert -- A Work in Progress
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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

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]

frequency, pitch, tone

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.

gases liquids solids
     
v =  ⎛
⎝		 B ⎞
⎠		 ½  =  ⎛
⎝		 γP ⎞
⎠		 ½  =  ⎛
⎝		 γkT ⎞
⎠		 ½
ρ ρ M
v =  ⎛
⎝		 B ⎞
⎠		 ½
ρ
v =  ⎛
⎝		 Y ⎞
⎠		 ½
ρ
           
B =  bulk modulus B =  bulk modulus Y =  young's modulus
ρ =  density ρ =  density ρ =  density
γ =  CP / CV (specific heat ratio)        
P =  absolute pressure        
k =  boltzmann's constant        
T =  absolute temperature        
M =  molecular mass        

 

Speed of Sound in Various Materials
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      
glass, crown 5100      
glass, flint 3980   gases (STP) v (m/s)
glass, pyrex 5640   air, 000 °C 331
gold 3240   air, 020 °C 343
granite 5950   argon 319
iron 5950   carbon dioxide 259
lead 2160   helium 965
lucite 2680   hydrogen (H2) 1284
marble 3810   neon 435
rubber, butyl 1830   nitrogen 334
rubber, vulcanized 54   nitrous oxide 263
silver 3650   oxygen (O2) 316
steel, mild 5960   water vapor, 134 °C 494
steel, stainless 5790      
titanium 6070   biological materials v (m/s)
wood, ash 4670   soft tissues 1540
wood, elm 4120      
wood, maple 4110      
wood, oak 3850      
Sources: Unknown, but probably an old version of the CRC

Acoustic Thermometry of Ocean Climates (ATOC)

echoes

scraps

frequency & wavelength

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 (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 - 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 sound in this range
1 - 5 tornadoes

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.

Frequency Hearing Ranges for Selected Animals (60 dB)
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

infrasound

ultrasound

Typical Parameters of Medical Ultrasound
  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
Source: Physics Today (December 2001)

human hearing

More in the next section.

Summary

Problems

practice

  1. Write something.
    • Answer it.
  2. Write something else.
    • Answer it.
  3. Write something different.
    • Answer it.
  4. Write something completely different.
    • Answer it.

numerical

  1. What range of wavelengths in air at room temperature are audible to a human with ideal hearing?
  2. Verify the claim that a 500 Hz sound wave in air has a wavelength approximately equal to the separation between the ears of a typical adult human.

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