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 Probs.Sound Probs.

1.1. What is the speed of sound in air if the temperature What is the speed of sound in air if the temperature is 306 K?is 306 K?

2.2. Find the f of a sound wave moving in air at room Find the f of a sound wave moving in air at room temp (20 C) with a wavelength of .667 m.temp (20 C) with a wavelength of .667 m.

3.3. What are the smallest and largest wavelengths that What are the smallest and largest wavelengths that the human ear can detect at 20 C?the human ear can detect at 20 C?

4.4. If you clap your hands and hear the echo from a If you clap your hands and hear the echo from a distant wall .20 s later, how far away is the wall?distant wall .20 s later, how far away is the wall?

5.5. What is the frequency of sound in air at 20 C What is the frequency of sound in air at 20 C having a wavelength equal to the diameter of a 38 having a wavelength equal to the diameter of a 38 cm woofer loud speaker? Of a 7.6 cm tweeter?cm woofer loud speaker? Of a 7.6 cm tweeter?

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 Aluminium 5100Copper 3800 Aluminium 5100

The human ear relatesThe human ear relatesamplitudeamplitude to to

loudnessloudnessandand

frequencyfrequency to topitchpitch..

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

Click here to make your own sound waves.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 here to view a Click here to view a simulationsimulation

of the refraction of sound of the refraction of sound waves.waves.

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

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.wavelengths.

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.

Oscilliscope video (saved in TAMU file)Oscilliscope video (saved in TAMU file) http://scientist.wetpaint.com/http://scientist.wetpaint.com/

page/'The+Speed+of+Sound+in+AIR+usipage/'The+Speed+of+Sound+in+AIR+using+RESONANCE'+Lab?t=anonng+RESONANCE'+Lab?t=anon

Sound and stringsSound and strings

Velocity depends on tension and mass per unit Velocity depends on tension and mass per unit length of the string.length of the string.

V=V=√(F√(FTT//μμ))

FFTT=Force of tension in string=Force of tension in string

μμ=mass/unit length of string=mass/unit length of stringA piano string is 1.10 m long and has a mass of 9.00 A piano string is 1.10 m long and has a mass of 9.00

g. How much tension must the string be under if it g. How much tension must the string be under if it is to vibrate at a fundamental frequency of 131 Hz? is to vibrate at a fundamental frequency of 131 Hz? What are the frequencies of the first four What are the frequencies of the first four harmonics?harmonics?

Click here to see a simulation ofClick 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 keys”between every two “white keys”on a piano keyboard?on a piano keyboard?

NoteNote FrequenFrequency (Hz)cy (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

NoteNote FrequenFrequency (Hz)cy (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