SOUNDSOUND a range of a range of compressioncompression

wavewavefrequencies to which thefrequencies to which thehuman earhuman ear is sensitive is sensitive

TheThe audio spectrumaudio spectrumextends from approximatelyextends from approximately

20 Hz20 Hz toto 20,000 Hz20,000 Hz..

Range of Some Common SoundsRange of Some Common Sounds

Intensity Range for Some Common SoundsIntensity Range for Some Common Sounds

Sounds are produced bySounds are produced byvibrating mattervibrating matter

1. reedsreeds

2. stringsstrings

3. membranesmembranes

4. air columnsair columns

Sound is a Sound is a mechanical wavemechanical wave (longitudinal). (longitudinal). It will It will notnot travel through a vacuum. travel through a vacuum.

Sounds possess the Sounds possess the characteristicscharacteristics

and and propertiesproperties that thatare common to allare common to all

waves.waves.

Just like all longitudinal (compression)Just like all longitudinal (compression)waves, sound waves possess awaves, sound waves possess a

velocityvelocity, , frequencyfrequency, , wavelengthwavelength,,phasephase, , periodperiod, and , and amplitudeamplitude..

Sound waves also Sound waves also reflectreflect, , refractrefract,,diffractdiffract, and , and interfereinterfere..

The velocity of sound in air The velocity of sound in air dependsdepends

on the air temperature. The speed on the air temperature. The speed ofof

sound in dry air is sound in dry air is 331.5 m/s331.5 m/s at at 0 0 ººCC.. This speedThis speed

increasesincreaseswith with

temperature: temperature: about about 0.6 m/s0.6 m/sfor every 1 for every 1 ººC C increase in increase in

temperature.temperature.

Sound generally travels Sound generally travels fastestfastest

in solids and slowest in in solids and slowest in gases,gases,

but there are some but there are some exceptions.exceptions.

Medium Velocity (m/s) Medium Velocity Medium Velocity (m/s) Medium Velocity (m/s)(m/s)

Air 330 Carbon dioxide 260Air 330 Carbon dioxide 260

Helium 930 Hydrogen 1270Helium 930 Hydrogen 1270

Oxygen 320 Water 1460Oxygen 320 Water 1460

Sea water 1520 Mercury 1450Sea water 1520 Mercury 1450

Glass 5500 Granite 5950Glass 5500 Granite 5950

Lead 1230 Pine wood 3320Lead 1230 Pine wood 3320

Copper 3800 Aluminum 5100Copper 3800 Aluminum 5100

The human ear relatesThe human ear relatesamplitudeamplitude to to

loudnessloudnessandand

frequencyfrequency to topitchpitch..

Listen to various sound frequencies Listen to various sound frequencies here and mixtures of sound waves here.and mixtures of sound waves here.

Click Click here to make your own sound waves.You should hear that frequencyYou should hear that frequency

relates to pitch and amplitude relatesrelates to pitch and amplitude relatesto loudness (for a given frequency).to loudness (for a given frequency).

Sound waves refract.Sound waves refract.

Click Click here to view a simulationof the refraction of sound of the refraction of sound

waves.waves.

The The interferenceinterference of sound of soundwaves can cause “beats”waves can cause “beats”

Click Click here and here to run computersimulations of interfering sound wavessimulations of interfering sound waves

that result in discernable beats.that result in discernable beats.

View interference “beats” View interference “beats” here and here.

What are evidences of What are evidences of reflectionreflectionand the and the diffractiondiffraction of sound? of sound?

All objects have a naturalAll objects have a natural

frequency of vibration.frequency of vibration.

ResonanceResonance - the inducing- the inducingof vibrations of a naturalof vibrations of a naturalrate by a vibrating sourcerate by a vibrating source

having the same frequencyhaving the same frequency

““sympathetic vibrations”sympathetic vibrations”

Famous Bridge Collapses:Famous Bridge Collapses:Evidences of Resonance?Evidences of Resonance?

Tacoma Narrows link Tacoma Narrows link Others linkOthers link

A resonant air column isA resonant air column issimply a standing simply a standing

longitudinallongitudinalwave system, much likewave system, much like

standing waves on a standing waves on a string.string. closed-pipe resonatorclosed-pipe resonator tube in which one end is tube in which one end is

openopenand the other end is closedand the other end is closed

open-pipe resonatoropen-pipe resonatortube in which both endstube in which both ends

are openare open

A A closed pipeclosed pipe resonates when resonates when the the length length

of the air columnof the air column is approximately is approximatelyan an odd numberodd number of of quarterquarter

wavelengths long.wavelengths long.

l = {(1,3,5,7,…)/4} *

With a slight correction for tube diameter,With a slight correction for tube diameter,we find that the resonant wavelength of awe find that the resonant wavelength of a

closed pipe is given by the formula:closed pipe is given by the formula:

= 4 (l + 0.4d),= 4 (l + 0.4d),

where where is the wavelength of sound, is the wavelength of sound,l is the length of the closed pipe,l is the length of the closed pipe,and d is the diameter of the pipe.and d is the diameter of the pipe.

An An open pipeopen pipe resonates when resonates when the the lengthlength

of the air columnof the air column is approximately is approximatelyan an even numbereven number of of quarterquarter

wavelengths long.wavelengths long.

l = {(2,4,6,8,…)/4} *

With a slight correction for tube diameter,With a slight correction for tube diameter,we find that the resonant wavelength of anwe find that the resonant wavelength of an

open pipe is given by the formula:open pipe is given by the formula:

= 2 (l + 0.8d),= 2 (l + 0.8d),

where where is the wavelength of sound, is the wavelength of sound,l is the length of the closed pipe,l is the length of the closed pipe,and d is the diameter of the pipe.and d is the diameter of the pipe.

Click Click here to see a simulation of standing waves in a resonant tubestanding waves in a resonant tube

(closed and open).(closed and open).

Learn more about resonance here.Learn more about resonance here.

Why aren’t there “black keys”Why aren’t there “black keys”between every two “white between every two “white

keys”keys”on a piano keyboard?on a piano keyboard?

Note Frequency (Hz)

AA 220220

BB 247247

CC 261.5261.5

DD 293.5293.5

EE 329.5329.5

FF 349349

GG 392392

AA 440440

BB 494494

CC 523523

DD 587587

EE 659659

FF 698698

GG 784784

Can you look at Can you look at this chart of this chart of notes andnotes andfrequencies for frequencies for the “white keys” the “white keys” and decide where and decide where “black keys” “black keys” should be should be placed?placed?

Now look at a graph of those values.Now look at a graph of those values.Does this graph help you decide?Does this graph help you decide?

Frequencies

200

300

400

500

600

700

800

A B C D E F G A B C D E F G

Frequencies

200

250

300

350

400

450

500

550

600

650

700

750

800

A Bb B C C# D Eb E F F# G Ab A Bb B C C# D Eb E F F# G

Note Frequency (Hz)

AA 220220

BB 247247

CC 261.5261.5

DD 293.5293.5

EE 329.5329.5

FF 349349

GG 392392

AA 440440

BB 494494

CC 523523

DD 587587

EE 659659

FF 698698

GG 784784