Kureba kwetambo, Kurema kwetambo, Kuwanda, uye Maitiro ekumanikidzwa kwetambo
Pengantar
Matambo chikamu chakakosha chezviridzwa zvakawanda zvemimhanzi, kubva kumagitare kusvika kumaviolin. Kureba, huremu, frequency, uye kusimba kwetambo zvinoita basa rakakosha pakuona kuti inzwi rayo rinonzwika sei uye mhando yeruzha rwainoburitsa. Muchinyorwa chino, tichakurukura kuti zviyero izvi zvine hukama sei kuburikidza nefizikisi uye kuti zvinoshanda sei mukuita, kunyanya mumamiriro ezviridzwa zvemimhanzi.
Kureba kwetambo
Kureba kwetambo (\(L\)) inhambwe iri pakati penzvimbo mbiri apo tambo inosungirirwa kana kubatwa. Muzviridzwa zvemimhanzi, hurefu uhwu hunowanzo kuyerwa kubva panzvimbo apo tambo inotanga kudedera kusvika painomira kudedera.
Kureba kwetambo kunokanganisa frequency yayo huru. Kazhinji, kureba kwetambo, ndiko kuderera kwefrequency yainoburitsa. Hukama huripo pakati pehurefu hwetambo nefrequency hunogona kuonekwa mu equation yekutanga yewave yakamira patambo:
\[ f = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Di mana:
– \( f \) ndiyo frequency (Hz),
– \( n \) ndiyo nhamba yeharmonic (1 ye fundamental frequency, 2 ye harmonic yechipiri, nezvimwewo),
– \( L \) kureba kwetambo (mita),
– \( T \) ndiko kusimba kwetambo (Newton),
– \( \mu \) huremu hwehuremu hwetambo (kg/m) payuniti imwe neimwe.
Tambo Yesimbi
Huremu hwetambo (\(m\)) huremu hwese hwetambo. Huremu hwehuremu hweyuniti (\(\mu\)) huremu hwetambo pamita imwe chete yehuremu hwetambo uye hunoratidzwa seizvi:
\[ \mu = \frac{m}{L} \]
Di mana:
– \( m \) huremu hwese hwetambo (kg),
– \( L \) kureba kwetambo (mita).
Huremu uhwu pahuniti hunokosha pakuona kuti tambo inodedera kakawanda sei. Kana tambo yakakura, frequency inogadzirwa netambo inoderera. Izvi zvinodaro nekuti tambo dzinorema dzinoda simba rakawanda kuti dzidedera pafrequency yakatarwa.
Kuwanda kwetambo
Frequency (\(f\)) inhamba yekudedera pasekondi inogadzirwa netambo. Frequency yekutanga (\(f_1\)) yetambo inodedera ndiyo frequency yakaderera uye inogona kuverengerwa uchishandisa fomura:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Kuwanda kweharmonic kunogonawo kuverengerwa uchishandisa fomura iyi, nekutsiva nhamba yeharmonic \(n\) mu equation:
\[ f_n = \frac{n}{2L} \sqrt{\frac{T}{\mu}} \]
Di mana:
– \( f_n \) ndiyo frequency ye nth harmonic (Hz),
– \( n \) inhamba inopindirana.
Kushushikana kweTambo
Kusimba (\(T\)) isimba rinoshandiswa patambo kuti isimbiswe. Kusimba uku kunoyerwa muNewtons (N) uye chinhu chakakosha chinosarudza kuti tambo inodedera kakawanda sei.
Kana kushushikana kwetambo kukawedzera, frequency yekudedera ichawedzerawo. Hukama uhwu hunogona kutsanangurwa uchishandisa formula ye frequency yataurwa pamusoro apa:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
Kubva pafomura iyi, tinogona kuona kuti frequency inoenderana zvakananga ne square root ye voltage. Izvi zvinoreva kuti kana voltage ikawedzerwa kaviri, frequency ichawedzera ne factor ye square root ye two.
Muenzaniso weKuverenga
Ngatitarisei mimwe mienzaniso yekuverenga kuti tinzwisise zviri nani hukama huripo pakati pehurefu hwetambo, huremu, frequency, uye tension.
Muenzaniso 1: Kuziva Kuwanda kweTambo
Ngatitii tine tambo ine urefu hwemita imwe, huremu hwese hwe 0.01 kg, uye kusimba kwe 100 N. Tinoda kuziva kuti tambo iyi inotenderera kakawanda sei.
1. Verenga huremu hwehurefu hweyuniti imwe neimwe:
\[ \mu = \frac{m}{L} = \frac{0.01}{1} = 0.01 \, \text{kg/m} \]
2. Shandisa fomura yekutanga yemafrequency:
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ f_1 = \frac{1}{2 \times 1} \sqrt{\frac{100}{0.01}} \]
\[ f_1 = \frac{1}{2} \sqrt{10000} \]
\[ f_1 = \frac{1}{2} \kawa 100 \]
\[ f_1 = 50 \, \mashoko{Hz} \]
Saka, frequency huru yetambo iyi i50 Hz.
Muenzaniso 2: Kuziva Voltage Inodiwa
Ngatitii tinoda kuona kumanikidzwa kunodiwa patambo ine hurefu hwemamita 0.5 uye huremu hwese hwe0.02 kg kuti ibudise frequency ye440 Hz (frequency yakajairwa yenoti A).
1. Verenga huremu hwehurefu hweyuniti imwe neimwe:
\[ \mu = \frac{m}{L} = \frac{0.02}{0.5} = 0.04 \, \text{kg/m} \]
2. Shandisa fomura ye frequency yekutanga uye gadzirisa \(T\):
\[ f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
\[ 440 = \frac{1}{2 \times 0.5} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \frac{1}{1} \sqrt{\frac{T}{0.04}} \]
\[ 440 = \sqrt{\frac{T}{0.04}} \]
\[ 440^2 = \frac{T}{0.04} \]
\[ 193600 = \frac{T}{0.04} \]
\[ T = 193600 \kawa 0.04 \]
\[ T = 7744 \, \mashoko{N} \]
Saka, voltage inodiwa kuti pave nefrequency yekutanga ye440 Hz i7744 N.
Maitiro Anoshanda
1. Zviridzwa zveMimhanzi
Matambiro anoshandiswa muzviridzwa zvakasiyana-siyana zvemimhanzi, kusanganisira magitare, maviolin, uye mapiyano. Kunzwisisa hukama huripo pakati pehurefu hwetambo, huremu, frequency, uye kumanikidzwa kwakakosha pakugadzirisa zviridzwa nemazvo uye kugadzira toni yaunoda.
2. Tekinoroji
Tambo dzinoshandiswawo muhunyanzvi hwemazuva ano, senge mumasensa nemidziyo yekuyera. Semuenzaniso, strain gauge inoshandisa shanduko mukumanikidzwa kwetambo kuyera deformation uye stress mune chinhu.
3. Tsvagiridzo neDzidzo
Mudzidzo netsvagiridzo yefizikisi, kuyedza netambo kunoshandiswa kudzidza mafungu nekudengenyeka. Izvi zvinobatsira vadzidzi kunzwisisa pfungwa huru mufizikisi yemafungu neacoustics.
Mhedziso
Kunzwisisa mafomati uye hukama huripo pakati pehurefu hwetambo, huremu, kuwanda, uye kumanikidzwa kwakakosha munzvimbo dzakawanda, kunyanya mimhanzi netekinoroji. Tichishandisa mafomati ekutanga efizikisi, tinogona kuverenga nekufanotaura maitiro etambo mumamiriro akasiyana-siyana, zvichitibatsira mukushandiswa kwakasiyana-siyana, kubva pakugadzirisa zviridzwa zvemimhanzi kusvika pakuyera kwakarurama mune tekinoroji yemazuva ano.
