Kutalika kwa Zingwe, Kulemera kwa Zingwe, Kuchuluka kwa Mafupipafupi, ndi Mafomula Olimbitsa Zingwe
Pegantar
Zingwe ndi gawo lofunika kwambiri pa zida zambiri zoimbira, kuyambira magitala mpaka ma violin. Kutalika, kulemera, kuchuluka kwa mawu, ndi mphamvu ya zingwe zimagwira ntchito yofunika kwambiri pozindikira kumveka bwino kwa mawu ndi mtundu wa mawu omwe amatulutsa. M'nkhaniyi, tikambirana momwe magawowa amagwirizanirana kudzera mu fizikisi ndi momwe amagwiritsidwira ntchito, makamaka pankhani ya zida zoimbira.
Utali wa Chingwe
Kutalika kwa chingwe (\(L\)) ndi mtunda pakati pa malo awiri pomwe chingwecho chimamangiriridwa kapena kugwiridwa. Mu zida zoimbira, kutalika kumeneku nthawi zambiri kumayesedwa kuyambira pomwe chingwecho chimayamba kugwedezeka mpaka pomwe chimasiya kugwedezeka.
Kutalika kwa chingwe kumakhudza ma frequency ake oyambira. Kawirikawiri, chingwe chikakhala chachitali, ma frequency omwe chimapanga amakhala otsika. Ubale pakati pa kutalika kwa chingwe ndi ma frequency ungawonekere mu equation yoyambira ya mafunde oyima pa chingwe:
\[ f = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Kumene:
– \( f \) ndi mafupipafupi (Hz),
– \( n \) ndi nambala ya harmonic (1 ya ma frequency oyambira, 2 ya harmonic yachiwiri, ndi zina zotero),
– \( L \) ndi kutalika kwa chingwe (mamita),
– \( T \) ndi mphamvu ya chingwe (Newton),
– \( \mu \) ndi kulemera kwa unit iliyonse ya unit ya chingwe (kg/m).
Chingwe Cholemera
Kulemera kwa chingwe (\(m\)) ndi kulemera konse kwa chingwe. Kulemera pa unit level (\(\mu\)) ndi kulemera kwa chingwe pa mita imodzi ya kutalika kwa chingwe ndipo kumafotokozedwa motere:
\[ \mu = \frac{m}{L} \]
Kumene:
– \( m \) ndi kulemera konse kwa chingwe (kg),
– \( L \) ndi kutalika kwa chingwe (mamita).
Kulemera kumeneku pa unit ndi kofunika kwambiri podziwa kuchuluka kwa kugwedezeka kwa chingwe. Chingwe chikakhala chachikulu, kuchuluka kwa ma frequency opangidwa ndi chingwecho kumakhala kochepa. Izi zili choncho chifukwa zingwe zolemera zimafuna mphamvu zambiri kuti zigwedezeke pa nthawi inayake.
Mafupipafupi a Zingwe
Mafupipafupi (\(f\)) ndi chiwerengero cha kugwedezeka pa sekondi iliyonse komwe kumapangidwa ndi chingwe. Mafupipafupi oyambira (\(f_1\)) a chingwe chogwedezeka ndi mafupipafupi otsika kwambiri ndipo amatha kuwerengedwa pogwiritsa ntchito fomula iyi:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Mafupipafupi a harmonic angawerengedwenso pogwiritsa ntchito fomula iyi, posintha nambala ya harmonic \(n\) mu equation:
\[ f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Kumene:
– \( f_n \) ndi kuchuluka kwa nth harmonic (Hz),
– \( n \) ndi nambala yogwirizana.
Kupsinjika kwa Zingwe
Kupsinjika (\(T\)) ndi mphamvu yomwe imagwiritsidwa ntchito pa chingwe kuti chikhale cholimba. Kupsinjika kumeneku kumayesedwa mu Newtons (N) ndipo ndi chinthu chofunikira chomwe chimatsimikizira kuchuluka kwa kugwedezeka kwa chingwe.
Ngati mphamvu ya chingwe ikuwonjezeka, kuchuluka kwa kugwedezeka kudzawonjezekanso. Ubale uwu ukhoza kufotokozedwa pogwiritsa ntchito njira yoyambira ya ma frequency yomwe yatchulidwa pamwambapa:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Kuchokera mu fomula iyi, titha kuwona kuti ma frequency ndi ofanana mwachindunji ndi muzu wa sikweya wa voltage. Izi zikutanthauza kuti ngati voltage yawirikiza kawiri, ma frequency adzawonjezeka ndi factor ya muzu wa sikweya wa awiri.
Chitsanzo cha Kuwerengera
Tiyeni tiwone zitsanzo zina za kuwerengera kuti timvetse bwino ubale womwe ulipo pakati pa kutalika kwa chingwe, kulemera, kuchuluka kwa chingwe, ndi kupsinjika.
Chitsanzo 1: Kudziwa Kuchuluka kwa Chingwe
Tiyerekeze kuti tili ndi chingwe chokhala ndi kutalika kwa mita imodzi, kulemera konse kwa 0.01 kg, ndi mphamvu ya 100 N. Tikufuna kudziwa kuchuluka kwa chingwe ichi.
1. Werengani kulemera pa utali uliwonse:
\[ \mu = \frac{m}{L} = \frac{0.01}{1} = 0.01 \, \text{kg/m} \]
2. Gwiritsani ntchito njira yoyambira yowerengera ma frequency:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ f_1 = \frac{1}{2 \times 1} \sqrt{\frac{100}{0.01}} \]
\[ f_1 = \frac{1}{2} \sqrt{10000} \]
\[ f_1 = \frac{1}{2} \nthawi 100 \]
\[ f_1 = 50 \, \malemba{Hz} \]
Chifukwa chake, ma frequency oyambira a chingwe ichi ndi 50 Hz.
Chitsanzo 2: Kudziwa Voltage Yofunikira
Tiyerekeze kuti tikufuna kudziwa mphamvu yofunikira pa chingwe chokhala ndi kutalika kwa mamita 0.5 ndi kulemera konse kwa 0.02 kg kuti chipange ma frequency oyambira a 440 Hz (ma frequency wamba a note A).
1. Werengani kulemera pa utali uliwonse:
\[ \mu = \frac{m}{L} = \frac{0.02}{0.5} = 0.04 \, \text{kg/m} \]
2. Gwiritsani ntchito njira yoyambira ya ma frequency ndikuthetsa \(T\):
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ 440 = \frac{1}{2 \times 0.5} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \frac{1}{1} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \sqrt{\frac{T}{0.04}} \]
\[ 440^2 = \frac{T}{0.04} \]
\[ 193600 = \frac{T}{0.04} \]
\[ T = 193600 \nthawi 0.04 \]
\[ T = 7744 \, \malemba{N} \]
Chifukwa chake, voteji yofunikira kuti pakhale ma frequency oyambira a 440 Hz ndi 7744 N.
Kugwiritsa Ntchito Mwanzeru
1. Zida Zoimbira
Zingwe zimagwiritsidwa ntchito mu zida zosiyanasiyana za nyimbo, kuphatikizapo magitala, ma vayolini, ndi ma piyano. Kumvetsetsa ubale womwe ulipo pakati pa kutalika kwa zingwe, kulemera, kuchuluka kwa mawu, ndi kupsinjika ndikofunikira kuti chida chikonzedwe bwino ndikupanga kamvekedwe kofunikira.
2. Ukadaulo
Zingwe zimagwiritsidwanso ntchito muukadaulo wamakono, monga mu masensa ndi zida zoyezera. Mwachitsanzo, choyezera cha strain chimagwiritsa ntchito kusintha kwa mphamvu mu chingwe poyesa kusintha ndi kupsinjika kwa chinthu.
3. Kafukufuku ndi Maphunziro
Mu maphunziro ndi kafukufuku wa sayansi ya zakuthambo, kuyesa ndi zingwe zimagwiritsidwa ntchito pophunzira mafunde ndi kugwedezeka. Izi zimathandiza ophunzira kumvetsetsa mfundo zazikulu mu sayansi ya zakuthambo ndi mawu.
Mapeto
Kumvetsetsa njira ndi ubale pakati pa kutalika kwa zingwe, kulemera, kuchuluka kwa zingwe, ndi kupsinjika ndikofunikira kwambiri m'magawo ambiri, makamaka nyimbo ndi ukadaulo. Pogwiritsa ntchito njira zoyambira za fizikisi, titha kuwerengera ndikulosera momwe zingwe zimagwirira ntchito m'mikhalidwe yosiyanasiyana, zomwe zimatithandiza pakugwiritsa ntchito njira zosiyanasiyana, kuyambira kusintha zida zoimbira mpaka kuyeza molondola muukadaulo wamakono.
