Post on 30-Dec-2015
description
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