Cov Qauv ntawm Txoj Hlua Ntev, Qhov Hlua Loj, Zaus, thiab Txoj Hlua Nruag
Pengantar
Cov hlua yog ib feem tseem ceeb ntawm ntau yam twj paj nruag, txij li guitars mus rau violins. Qhov ntev, qhov hnyav, zaus, thiab qhov nruj ntawm ib txoj hlua ua lub luag haujlwm tseem ceeb hauv kev txiav txim siab lub suab thiab qhov zoo ntawm lub suab uas nws tsim tawm. Hauv tsab xov xwm no, peb yuav tham txog seb cov kev ntsuas no cuam tshuam li cas rau ib leeg los ntawm physics thiab lawv siv li cas hauv kev xyaum, tshwj xeeb tshaj yog nyob rau hauv cov ntsiab lus ntawm cov twj paj nruag.
Qhov Ntev ntawm Txoj Hlua
Qhov ntev ntawm ib txoj hlua (\(L\)) yog qhov deb ntawm ob qho chaw uas txoj hlua khi lossis tuav. Hauv cov twj paj nruag, qhov ntev no feem ntau yog ntsuas los ntawm qhov chaw uas txoj hlua pib co mus rau qhov chaw uas nws tsis co lawm.
Qhov ntev ntawm ib txoj hlua cuam tshuam rau nws qhov zaus tseem ceeb. Feem ntau, txoj hlua ntev npaum li cas, qhov zaus uas nws tsim tawm yuav qis dua. Kev sib raug zoo ntawm qhov ntev ntawm txoj hlua thiab zaus tuaj yeem pom hauv cov qauv yooj yim rau nthwv dej sawv ntawm ib txoj hlua:
\[ f = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Qhov twg:
- \( f \) yog zaus (Hz),
- \( n \) yog tus lej harmonic (1 rau qhov zaus tseem ceeb, 2 rau qhov thib ob harmonic, thiab lwm yam),
- \( L \) yog qhov ntev ntawm txoj hlua (meters),
- \( T \) yog lub zog ntawm txoj hlua (Newton),
- \( \mu \) yog qhov hnyav ib chav ntev ntawm txoj hlua (kg/m).
String Mass
Qhov hnyav ntawm txoj hlua (\(m\)) yog qhov hnyav tag nrho ntawm txoj hlua. Qhov hnyav ib chav ntev (\(\mu\)) yog qhov hnyav ntawm txoj hlua ib 'meter' ntawm txoj hlua thiab yog qhia ua:
\[ \mu = \frac{m}{L} \]
Qhov twg:
- \(m\) yog tag nrho qhov hnyav ntawm txoj hlua (kg),
- \( L \) yog qhov ntev ntawm txoj hlua (meters).
Qhov hnyav no ib chav ntev yog qhov tseem ceeb heev rau kev txiav txim siab qhov zaus ntawm txoj hlua co. Qhov loj dua \(\mu\), qhov zaus qis dua uas txoj hlua tsim tawm. Qhov no yog vim tias cov hlua hnyav dua xav tau lub zog ntau dua los co ntawm qhov zaus uas tau muab.
Zaus ntawm cov hlua
Zaus (\(f\)) yog tus naj npawb ntawm kev co ib ob uas tsim los ntawm ib txoj hlua. Lub zaus tseem ceeb (\(f_1\)) ntawm ib txoj hlua co yog qhov zaus qis tshaj plaws thiab tuaj yeem suav los ntawm kev siv cov mis:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Tus zaus harmonic kuj tseem tuaj yeem suav tau siv cov mis no, los ntawm kev hloov tus lej harmonic \(n\) hauv kab zauv:
\[ f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Qhov twg:
- \( f_n \) yog zaus ntawm nth harmonic (Hz),
- \( n \) yog tus lej harmonic.
Kev nruj ntawm txoj hlua
Qhov nruj (\(T\)) yog lub zog uas siv rau ntawm txoj hlua kom nws nruj. Qhov kev nruj no ntsuas hauv Newtons (N) thiab yog ib qho tseem ceeb uas txiav txim siab qhov zaus ntawm kev co ntawm txoj hlua.
Yog tias qhov nro ntawm txoj hlua nce ntxiv, qhov zaus ntawm kev co kuj yuav nce ntxiv. Qhov kev sib raug zoo no tuaj yeem piav qhia siv cov qauv zaus tseem ceeb uas tau hais los saum toj no:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Los ntawm cov mis no, peb tuaj yeem pom tias zaus yog ncaj qha proportional rau cov hauv paus plaub fab ntawm lub voltage. Qhov no txhais tau tias yog tias lub voltage yog ob npaug, qhov zaus yuav nce los ntawm ib qho ntawm cov hauv paus plaub fab ntawm ob.
Piv txwv kev xam
Cia peb saib qee qhov piv txwv kev xam kom nkag siab zoo dua txog kev sib raug zoo ntawm txoj hlua ntev, qhov hnyav, zaus, thiab qhov nruj.
Piv txwv 1: Txheeb xyuas qhov zaus ntawm ib txoj hlua
Xav tias peb muaj ib txoj hlua uas ntev li 1 'meter', tag nrho qhov hnyav yog 0.01 kg, thiab qhov nruj yog 100 N. Peb xav txiav txim siab qhov zaus tseem ceeb ntawm txoj hlua no.
1. Xam qhov hnyav ib chav ntev:
\[ \mu = \frac{m}{L} = \frac{0.01}{1} = 0.01 \, \text{kg/m} \]
2. Siv cov qauv zaus yooj yim:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ f_1 = \frac{1}{2 \times 1} \sqrt{\frac{100}{0.01}} \]
\[ f_1 = \frac{1}{2} \sqrt{10000} \]
\[ f_1 = \frac{1}{2} \times 100 \]
\[ f_1 = 50 \, \text{Hz} \]
Yog li, qhov zaus tseem ceeb ntawm txoj hlua no yog 50 Hz.
Piv txwv 2: Txheeb xyuas qhov Voltage uas xav tau
Xav tias peb xav txiav txim siab qhov nro uas xav tau rau ib txoj hlua uas ntev li 0.5 meters thiab tag nrho qhov hnyav ntawm 0.02 kg los tsim kom muaj zaus tseem ceeb ntawm 440 Hz (zaus txheem ntawm lub cim A).
1. Xam qhov hnyav ib chav ntev:
\[ \mu = \frac{m}{L} = \frac{0.02}{0.5} = 0.04 \, \text{kg/m} \]
2. Siv cov qauv zaus tseem ceeb thiab daws rau \(T\):
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ 440 = \frac{1}{2 \times 0.5} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \frac{1}{1} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \sqrt{\frac{T}{0.04}} \]
\[ 440^2 = \frac{T}{0.04} \]
\[ 193600 = \frac{T}{0.04} \]
\[ T = 193600 \times 0.04 \]
\[ T = 7744 \, \text{N} \]
Yog li, qhov hluav taws xob uas xav tau los tsim kom muaj qhov zaus tseem ceeb ntawm 440 Hz yog 7744 N.
Cov Kev Siv Tau Zoo
1. Cov Cuab Yeej Suab Paj Nruag
Cov hlua siv rau hauv ntau yam twj paj nruag, suav nrog guitars, violins, thiab pianos. Kev nkag siab txog kev sib raug zoo ntawm qhov ntev ntawm cov hlua, qhov hnyav, zaus, thiab kev nruj yog qhov tseem ceeb rau kev kho kom zoo thiab tsim cov suab nrov xav tau.
2. Kev Siv Tshuab
Cov hlua kuj siv rau hauv cov thev naus laus zis niaj hnub no, xws li hauv cov sensors thiab cov khoom siv ntsuas. Piv txwv li, lub ntsuas qhov siab siv cov kev hloov pauv ntawm qhov nro hauv ib txoj hlua los ntsuas qhov deformation thiab kev ntxhov siab hauv cov khoom siv.
3. Kev Tshawb Fawb thiab Kev Kawm
Hauv kev kawm txog physics thiab kev tshawb fawb, kev sim nrog cov hlua yog siv los kawm txog cov nthwv dej thiab kev co. Qhov no pab cov tub ntxhais kawm nkag siab txog cov ntsiab lus tseem ceeb hauv wave physics thiab acoustics.
Xaus
Kev nkag siab txog cov qauv thiab kev sib raug zoo ntawm qhov ntev ntawm cov hlua, qhov hnyav, zaus, thiab qhov nruj yog qhov tseem ceeb heev rau ntau qhov chaw, tshwj xeeb tshaj yog suab paj nruag thiab thev naus laus zis. Siv cov qauv yooj yim ntawm physics, peb tuaj yeem xam thiab kwv yees tus cwj pwm ntawm cov hlua nyob rau hauv ntau yam mob, pab peb hauv ntau yam kev siv, los ntawm kev kho cov twj paj nruag mus rau kev ntsuas qhov tseeb hauv thev naus laus zis niaj hnub no.
