Ngā Tauira Pātai Kōrero mō te Ngaruiti
Ko ngā ngaruiti he wāhanga o te whānuitanga hikohiko, ā, ko ngā roangaru mai i te 1 mm ki te 1 m. He maha ngā whakamahinga o ēnei ngaru i roto i ngā hangarau hou, pērā i ngā whakawhitiwhiti kōrero ahokore, te radar, te whetū, me ngā taputapu whare pērā i ngā oumu ngaruiti. I te mea he mea nui ngā tono ngaruiti, he mea nui kia mārama ngā ākonga, inā koa ko te hunga e ako ana i te ahupūngao, i te hangarau rānei, ki ngā kaupapa matua o ngā ngaruiti, tae atu ki te whakaoti rapanga e pā ana ki aua rapanga. Ka matapakihia e tēnei tuhinga ētahi tauira rapanga me ngā ngaruiti.
Pātai 1: Te Roanga Ngaru me te Auautanga
Pātai:
Ki te mea he 10 GHz te auau o te ngaruiti, tatauhia te roangaru o te ngaruiti. (Whakamahia te tere o te mārama c = 3 x 10^8 m/s)
Kōrero:
Tuatahi, ka maumahara tātou ki te whanaungatanga i waenga i te roangaru (λ), te auau (f), me te tere o te mārama (c):
\[ c = \lambda \cdot f \]
Ka taea e tātou te whakahoki anō i tēnei tātai hei kimi i te roanga ngaru (λ):
\[ \lambda = \frac{c}{f} \]
Mēnā he auau (f) = 10 GHz = 10 x 10^9 Hz, me te tere o te mārama (c) = 3 x 10^8 m/s, ka tāpirihia ēnei uara e rua ki te tātai:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10 \times 10^9 \, \text{Hz}} \]
\[ \lambda = 0.03 \, \text{m} \]
Nō reira, ko te roanga ngaru o te ngaruiti he 0,03 mita, arā, 3 cm.
Pātai 2: Te Tuku Mana me te Tawhiti
Pātai:
Ka tukuna e te tuku hiko ngaruiti te mana o te 50 W. Tātaihia te kaha o te ngaruiti i te tawhiti o te 2 mita mai i te pūtake tuku, me te whakaaro ko te horapa isotropic.
Kōrero:
Hei tatau i te kaha, ka whakamahia e mātou te whārite mana mō ia waeine horahanga:
\[ I = \frac{P}{A} \]
Ko P te mana (50 W) ā, ko A te horahanga mata o te porowhita he 2 mita te whānui:
\[ A = 4 \pi r^2 \]
Tāuruhia te uara r = 2 mita ki te tātai horahanga:
\[ A = 4 \pi (2 \, \text{m})^2 \]
\[ A = 16 \pi \, \text{m}^2 \]
Kātahi ka tatau i te kaha:
\[ I = \frac{50 \, \text{W}}{16 \pi \, \text{m}^2} \]
Te tatau i ngā uara tau:
\[ Ahau \tata \frac{50}{50.265} \]
\[ I \tata ki te 0.995 \, \kuputuhi{W/m}^2 \]
Nō reira, ko te kaha o te ngaruiti i te tawhiti o te 2 mita mai i te pūtake tuku he tata ki te 0.995 W/m².
Pātai 3: Te Pānga Doppler i roto i ngā Ngaruiti
Pātai:
E whakatata atu ana tētahi waka e tere ana i te 108 km/h (30 m/s) ki tētahi radar e tuku ana i ngā ngaruiti i te auau o te 5 GHz. Tātaihia te auau ka riro mai i te radar mēnā ko te tere o te ngaruiti te tere o te mārama.
Kōrero:
Whakamahia te pānga Doppler mō te auau i whiwhihia (f'):
\[ f' = f \left(\frac{c + v}{c}\right) \]
Kei hea:
– f' = te auau whiwhi
– f = auau pūtake = 5 GHz = 5 x 10^9 Hz
– c = te tere o te mārama = 3 x 10^8 m/s
– v = te tere o te waka = 30 m/s
Whakakapia ngā uara ki roto i te tātai:
\[ f' = 5 \times 10^9 \left(\frac{3 \times 10^8 + 30}{3 \times 10^8}\right) \]
\[ f' \approx 5 \times 10^9 \left(1 + \frac{30}{3 \times 10^8}\right) \]
\[ f' \approx 5 \times 10^9 \left(1 + 1 \times 10^{-7}\right) \]
\[ f' \tata ki te 5 \whakaahua 10^9 \whakaahua 1.0000001 \]
\[ f' \tata ki te 5.0000005 \whakareatia ki te 10^9 \]
\[ f' \tata ki te 5.0000005 \, \kuputuhi{GHz} \]
Nō reira, ko te auau e whiwhihia ana e te radar he tata ki te 5.0000005 GHz.
Pātai 4: Te mimiti mana e ngā rauemi
Pātai:
Ka mimitihia e tētahi rauemi te 2 W o te mana ngaruiti ina ko te kaha o te ngaru taunga he 10 W/m². Tātaihia te horahanga o te mata o te rauemi.
Kōrero:
Whakamahia te whanaungatanga i waenga i te kaha mimiti me te horahanga mata me te kaha:
\[ P = I \cdot A \]
Whakakapia ngā uara e mōhiotia ana:
\[ 2 \, \kuputuhi{W} = 10 \, \kuputuhi{W/m}^2 \cdot A \]
Te whakaoti rapanga mō A:
\[ A = \frac{2 \, \text{W}}{10 \, \text{W/m}^2} \]
\[ A = 0.2 \, \text{m}^2 \]
Nō reira, ko te horahanga o te mata o te rauemi he 0,2 m².
Pātai 5: Ngā Tauira Whakaaroaro me te Whakararuraru
Pātai:
E rua ngā pūihi ngaruiti e tuku ana i ngā ngaru he 6 cm te roa i te ahunga kotahi. Mēnā he 12 cm te tawhiti i waenganui i ngā pūihi, i tēhea wāhi ka puta tuatahi mai te wawaotanga hangahanga?
Kōrero:
Ka puta te pokanoa hangahanga ina ko te rerekētanga ara i waenga i ngā pūtake e rua ko k = ±nλ (he tauoti kore-kore a n tae atu ki te 0). Mō te wā tuatahi ka puta te pokanoa hangahanga (n=1):
\[ d = n \lambda/2 \]
Nā te mea he 12 cm te tawhiti o te pūihi, ā, he 6 cm te roanga ngaru, ka puta te rerekētanga ara mō te pokanoa hanga tuatahi i:
\[ d = n (\lambda/2) \]
Nā reira:
\[ 12 = 1 \times (6/2) \]
Nā, ko te tawhiti e tū ana ko:
\[ 12 = 1 \whakareatia ki te 3 \]
Nā te mea e pā ana tēnei whārite ki te hanganga o ngā tauira pokanoa i runga i te mea whānui, nō reira, mai i te whakaaro ka hoahoahia e mātou i runga i te rārangi pokapū o te tawhiti mai i te pūtake, i te ara rānei, i runga i te ara kore-ara, arā, te tūranga pūmau o te rārangi tohu kāore e pā ana ki te tauira tūranga pumau kua whakaarohia.
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Anei ētahi tauira o ngā raruraru ngaruiti me pēhea te whakaoti. Mā te mārama me te taunga ki te whakaoti rapanga pēnei, ko te tumanako ka māmā ake māu te hopu me te whakamahi i ngā ariā ngaruiti i roto i ngā momo mara o te pūtaiao me te hangarau.
