[{"data":1,"prerenderedAt":61},["ShallowReactive",2],{"q-105170-arch_environment-15":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-105170-801-0104-015","architect","105170",105,"建築環境控制",15,null,"某點距離點音源 2 m 之音壓級為 80 dB，將此音源之音響功率增至 2 倍，且與音源之距離拉長至 4 m，則該點音壓級會變為多少？",{"A":14,"B":15,"C":16,"D":17},"74 dB","77 dB","80 dB","83 dB",[19],"B","single",[],"本題考點：點音源在自由音場中的音壓級，隨音響功率以 10 log 的關係增加、隨距離以 20 log 的關係衰減（逆平方定律）；兩個變化同時發生時，分別算出增減量再相加。\n【正解理由】點音源的音壓級變化量 ΔL = 10 log(W₂ \u002F W₁) − 20 log(r₂ \u002F r₁)。音響功率增至 2 倍，W₂ \u002F W₁ = 2，音壓級增加 10 log 2 = 10 × 0.301 dB；距離由 2 m 拉長到 4 m，r₂ \u002F r₁ = 4 \u002F 2 = 2，音壓級減少 20 log 2 = 20 × 0.301 dB。兩者合計 ΔL = 10 × 0.301 − 20 × 0.301 = −3.01 dB，原本 80 dB 變為 80 − 3.01 = 76.99 dB，取整數為 77 dB，與選項 (B) 相符，故選 B。\n【逐項排除】\n(A) 74 dB：不符合題目所問。這個數值只扣了距離加倍的衰減、沒有加回功率加倍的增量：80 − 20 × 0.301 = 73.98 dB，取整數為 74 dB。題目同時改變了功率與距離，兩項都要計入，加上功率增量後才是 77 dB。\n(B) 77 dB：符合題目所問。功率加倍增加 10 × 0.301 dB、距離加倍衰減 20 × 0.301 dB，相加後由 80 dB 降為 76.99 dB，取整數為 77 dB。\n(C) 80 dB：不符合題目所問。音壓級維持不變，代表功率增量與距離衰減剛好互相抵消；若把距離衰減也用 10 log 計算，就會得到 80 + 10 × 0.301 − 10 × 0.301 = 80 dB。點音源的音壓與距離成反比、音響強度與距離平方成反比，距離項必須用 20 log，衰減量是功率增量的兩倍，兩者不會抵消，結果是 77 dB。\n(D) 83 dB：不符合題目所問。這個數值只計入了功率加倍的增量、忽略距離拉長的衰減：80 + 10 × 0.301 = 83.01 dB，取整數為 83 dB。受音點已由 2 m 移到 4 m，距離衰減必須扣除，結果才是 77 dB。\n【演算步驟】\n公式：ΔL = 10 log(W₂ \u002F W₁) − 20 log(r₂ \u002F r₁)\n① 功率比 W₂ \u002F W₁ = 2，功率增量 = 10 log 2 = 10 × 0.301 dB\n② 距離比 r₂ \u002F r₁ = 4 m \u002F 2 m = 2，距離衰減 = 20 log 2 = 20 × 0.301 dB\n③ ΔL = 10 × 0.301 dB − 20 × 0.301 dB = −3.01 dB\n④ L₂ = 80 dB − 3.01 dB = 76.99 dB，取整數為 77 dB\n【記憶點】點音源：功率乘 2 用 10 log 加，距離乘 2 用 20 log 減，一加一減淨降約一半的距離衰減量。",603,1,true,[27,30,33,36,39,42],{"number":28,"session":7,"stem":29},12,"下列揮發性有機化合物，何者之沸點最低？",{"number":31,"session":7,"stem":32},13,"下列有關於日照時間的敘述，何者正確？",{"number":34,"session":7,"stem":35},14,"有關單層隔音構造質量法則之敘述，下列何者錯誤？",{"number":37,"session":7,"stem":38},16,"有關電氣音響系統不產生迴授音（howling）之設計條件敘述，下列何者錯誤？",{"number":40,"session":7,"stem":41},17,"下列建築聲學單位之敘述，何者錯誤？",{"number":43,"session":7,"stem":44},18,"有關建築物之污水排放濃度及污水處理設備性能指標之敘述，下列何者正確？",[46,49,52,55,58],{"number":10,"session":47,"stem":48},"114180","有關建築牆構造之隔音性能，下列敘述何者錯誤？",{"number":10,"session":50,"stem":51},"113190","某牆壁面積為 15 m2，其中包含一樘玻璃窗，面積 2.4 m2，500 Hz 吸音…",{"number":10,"session":53,"stem":54},"112190","下列關於相對濕度的敘述何者錯誤？",{"number":10,"session":56,"stem":57},"111180","有關多孔質吸音材料的吸音特性敘述，下列何者錯誤？",{"number":10,"session":59,"stem":60},"110180","某鋼筋混凝土屋頂構造，計算屋頂平均熱傳透率 Uar 時，不包括下列那個項目？",1791863214183]