[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-112190-arch_environment-6":3},{"question":4,"neighbors":26,"sameNumber":45,"prev":34,"next":37},{"id":5,"classKey":6,"session":7,"year":8,"subject":9,"number":10,"groupStem":11,"ownStem":12,"stem":12,"options":13,"answer":18,"answerKind":20,"answerS":11,"answerNote":11,"images":21,"explanation":22,"withheld":11,"deepChars":23,"freq":24,"indexable":25},"arch-112190-801-0104-006","architect","112190",112,"建築環境控制",6,null,"小巨蛋演唱會彩排進行時，舞台上 3 組分散式監聽揚聲器同時驅動，測得聲壓級均為 80 dB，試算舞台上所測得總聲能最接近多少 dB？",{"A":14,"B":15,"C":16,"D":17},"80","85","90","95",[19],"B","single",[],"本題考點：多個聲源同時發聲時的聲壓級合成——分貝是對數量，不能直接相加，必須先換回聲能相加，再取對數；n 個相同聲壓級 L 的聲源合成後為 L + 10 log n。\n【正解理由】分貝的定義是 L = 10 log(I \u002F I₀)，代表的是聲能（聲強）相對於基準值的對數比。三組揚聲器分散擺放、彼此不相干，它們的聲能可以直接相加，但分貝值不行。每組 80 dB，相當於聲能比為 10 的 8 次方（80 \u002F 10 = 8），三組合計為 3 × 100000000 = 300000000；再取對數得 10 × log(300000000) = 10 × (8 + 0.477) = 84.77 dB，其中 0.477 為 log 3 的近似值。等價的簡式是 80 + 10 log 3 = 80 + 4.77 = 84.77 dB，最接近 85 dB，與選項 (B) 相符，故選 B。\n【逐項排除】\n(A) 80 dB：等於把三組聲源合成後的總聲壓級當成與單一聲源相同，忽略了聲能是會相加的；三組同時發聲，總聲能比單組大，總聲壓級應高於 80 dB，約為 84.77 dB。\n(B) 85 dB：先把每組 80 dB 換成聲能、三組相加後再取對數，得 84.77 dB，四捨五入最接近 85 dB，為本題所求。\n(C) 90 dB：高於正確值 84.77 dB 甚多，等於高估了三組聲源合成後的增量；三組相同聲壓級的聲源合成，只比單組多出 10 log 3，也就是 4.77 dB。\n(D) 95 dB：比 (C) 更高，高估更明顯；正確的合成結果仍為 84.77 dB，最接近 85 dB。\n【演算步驟】\n公式：L總 = 10 log(Σ10^(Li\u002F10))；n 個相同聲壓級 L 時，L總 = L + 10 log n\n換成聲能比：80 dB \u002F 10 = 8，每組聲能比為 100000000\n聲能相加：3 × 100000000 = 300000000\n取對數：L總 = 10 × (8 + 0.477) dB = 84.77 dB\n驗算：80 dB + 10 × 0.477 dB = 80 dB + 4.77 dB = 84.77 dB\n結果：最接近 85 dB\n【記憶點】分貝相加先換聲能：相同聲源 n 個，就是單一聲源的分貝數加上 10 log n。",611,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},3,"有關綠建材標章之防音綠建材評估要項，下列敘述何者正確？",{"number":31,"session":7,"stem":32},4,"有關無障礙廁所盥洗室之說明，下列何者錯誤？",{"number":34,"session":7,"stem":35},5,"單層均質材料的隔音性能與面密度有關，在質量控制頻域下，依質量法則（Mass Law）…",{"number":37,"session":7,"stem":38},7,"有關室內空氣污染物產生之來源，下列敘述何者錯誤？",{"number":40,"session":7,"stem":41},8,"在一座游泳池體育館中，有關體育館餘（迴）響時間的敘述，下列何者錯誤？",{"number":43,"session":7,"stem":44},9,"有關音樂廳內的回音產生原因與解決方法的敘述，下列何者錯誤？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","下列空間何者較適合安裝分離式冷氣機空調系統？",{"number":10,"session":50,"stem":51},"113190","某空間室內高度 2.5 m、面積 200 m2，為了達到良好的室內空氣品質，提出每小…",{"number":10,"session":53,"stem":54},"111180","當某餐廳的外部環境空氣品質良好時，下列何者不是室內空氣品質的主要評估項目？",{"number":10,"session":56,"stem":57},"110180","某材料的入射音能為 Ii、反射音能為 Ir、吸收音能為 Ia、傳透音能為 It，有關…",{"number":10,"session":59,"stem":60},"109180","有關風力換氣之敘述，何者錯誤？",1791863200921]