[{"data":1,"prerenderedAt":186},["ShallowReactive",2],{"topic-page:\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Fstanding-waves-nodes-and-antinodes":3},{"topic":4,"category":151,"seo":155,"breadcrumbs":160,"prerequisites":167,"nextTopics":177,"relatedTopics":185},{"id":5,"slug":6,"title":7,"summary":8,"canonicalPath":9,"categoryPath":10,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"generatedAt":14,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":16,"expectedKnowledge":22,"learningGoal":26,"blocks":27},"high-school-basic-physics-wave-standing-waves-nodes-and-antinodes","standing-waves-nodes-and-antinodes","定在波の節と腹","互いに逆向きへ進む同じ波の重ね合わせから、動かない節と大きく振動する腹をもつ定在波を読みます。","\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Fstanding-waves-nodes-and-antinodes","\u002Fhigh-school\u002Fbasic-physics\u002Fwave","beginner","student_high",6,"2026-07-28","ai_generated",[17,18,19,20,21],"物理基礎","波","定在波","節","腹",[23,24,25],"重ね合わせ","波の反射","波長","定在波の節・腹を見分け、節間・腹間・節腹間の距離から波長を求められるようになる。",[28,33,42,65,75,81,90,96,102,118,132,141],{"id":29,"type":30,"title":7,"subtitle":31,"shortDefinition":32},"hero","HeroBlock","波形は進まず、場所ごとの振れ幅が決まる","入射波と反射波が同じ振動数で逆向きに進むと、山が横へ移動しないように見える模様ができます。いつも動かない点を節、大きく振動する点を腹と呼びます。",{"id":34,"type":35,"term":19,"definition":36,"plainExplanation":37,"keywords":38},"definition","DefinitionBlock","同じ振幅・振動数の二つの波が逆向きに進んで重なり、節と腹の位置が空間に固定された波です。","節では二つの波が常に打ち消し合い、変位は0です。腹では強め合って振幅が最大になります。曲線全体が左右へ進むのではなく、各場所が固有の振幅で上下します。",[39,40,41],"節は変位0","腹は振幅最大","模様は進まない",{"id":43,"type":44,"title":45,"formulas":46,"strategy":64},"formula","FormulaBlock","節と腹の距離",[47,55],{"label":48,"expression":49,"meaning":50,"symbols":51},"隣り合う節または腹","距離=λ\u002F2","節から次の節、腹から次の腹までは半波長です。",[52],{"symbol":53,"meaning":54},"λ","もとの進行波の波長",{"label":56,"expression":57,"meaning":58,"symbols":59,"tip":63},"隣り合う節と腹","距離=λ\u002F4","節とそのすぐ隣の腹の間は四分の一波長です。",[60],{"symbol":61,"meaning":62},"λ\u002F4","一波長の四分の一","節と腹を交互にλ\u002F4ずつ置くと作図できます。","動かない点を節として印し、節同士の距離を2倍してλを求めます。",{"id":66,"type":67,"title":68,"points":69,"body":74},"key-points","KeyPointBlock","瞬間の交点と節を区別する",[70,71,72,73],"節はどの時刻でも動かない","腹は振幅が最大だが瞬間的に0を通る","節と腹はλ\u002F4ごとに交互に並ぶ","定在波の模様自体は進行しない","ある瞬間に基準線上にある点がすべて節なのではありません。時間がたっても常に変位0であり続ける位置だけが節です。",{"id":76,"type":77,"src":78,"alt":79,"caption":80},"diagram","DiagramBlock","\u002Fassets\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Fstanding-waves-nodes-and-antinodes\u002Fstanding-waves-nodes-and-antinodes.svg","定在波の上下二つの極端な形と、動かない節、大きく振動する腹、節間の半波長を示した図","実線と破線は半周期ずれた定在波の形です。両方が交わる黒い菱形が常に変位0の節、中央の両矢印が腹で、隣り合う節の間隔はλ\u002F2です。",{"id":82,"type":83,"steps":84,"title":89},"steps","StepBlock",[85,86,87,88],"時間が変わっても動かない位置を節とする","隣り合う節同士の距離を測る","その距離を2倍して波長λを出す","必要ならv=fλへつなぐ","図から波長を読む手順",{"id":91,"type":92,"scenario":93,"explanation":94,"result":95},"example","ExampleBlock","定在波で隣り合う節の間隔が0.30 m、振動数が8.0 Hzだった。","節間はλ\u002F2なので、λ=2×0.30=0.60 mです。もとの進行波の速さはv=fλ=8.0×0.60=4.8 m\u002Fsです。定在波の模様が進む速さではなく、重なっている二つの進行波の速さを求めています。","波長は0.60 m、進行波の速さは4.8 m\u002Fsです。",{"id":97,"type":98,"warningTitle":99,"message":100,"severity":97,"action":101},"warning","WarningBlock","節間を一波長としない","隣り合う節の間には定在波の形の半波長分が入り、空間距離はλ\u002F2です。","一波長には節間が二つ入ることを図の目盛りで確認します。",{"id":103,"type":104,"title":105,"questions":106},"quiz","QuizBlock","確認テスト",[107],{"question":108,"choices":109,"answerIndex":113,"choiceExplanations":114},"定在波で、ある節からすぐ隣の腹までの距離が0.20 mです。波長はどれですか。",[110,111,112],"0.80 m","0.40 m","0.20 m",0,[115,116,117],"正解です。節と隣の腹の距離はλ\u002F4なので、0.20×4=0.80 mです。","0.40 mは節間を0.20 mと取り違えた値です。","節と腹の距離をそのまま一波長にはできません。",{"id":119,"type":104,"title":120,"questions":121},"quiz-node","節の判定",[122],{"question":123,"choices":124,"answerIndex":113,"choiceExplanations":128},"ある瞬間に定在波が基準線を横切る位置を見つけました。その情報だけで節と断定できますか。",[125,126,127],"できない。時間がたっても常に変位0か確認する","できる。基準線上の点はすべて節","できる。腹も常に基準線上にある",[129,130,131],"正解です。節はどの時刻でも変位0の位置です。一枚の瞬間図だけでは追加確認が必要です。","腹を含む全ての点が、振動の途中で瞬間的に基準線を通ることがあります。","腹は振幅が最大の位置で、時間とともに上下へ大きく動きます。",{"id":133,"type":134,"title":135,"points":136},"summary","SummaryBlock","まとめ",[137,138,139,140],"定在波は逆向きの同じ波の重ね合わせでできる","節は常に変位0、腹は振幅最大","節間・腹間はλ\u002F2","隣り合う節と腹の間はλ\u002F4",{"id":142,"type":143,"title":144,"nextTopics":145,"relatedKeywords":147},"next-action","NextActionBlock","波の量を音の聞こえ方へ結び付ける",[146],"high-school-basic-physics-wave-sound-properties-and-waveform",[148,149,150],"音波","音の高さ","音の大きさ",{"path":10,"title":18,"description":152,"parentPath":153,"accentToken":154},"物理基礎の中でも、波の伝わり方や音の性質を扱うトピックを整理していくカテゴリです。","\u002Fhigh-school\u002Fbasic-physics","signal-blue",{"title":156,"description":157,"canonicalUrl":158,"ogImage":159},"定在波の節と腹 | 物理基礎","反射波との重ね合わせで生じる定在波を、節・腹と波長の距離関係から学びます。","https:\u002F\u002Fzeqnilo.com\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Fstanding-waves-nodes-and-antinodes","https:\u002F\u002Fzeqnilo.com\u002Fassets\u002Fsite\u002Fdefault-og.svg",[161,164,165,166],{"title":162,"path":163},"高校","\u002Fhigh-school",{"title":17,"path":153},{"title":18,"path":10},{"title":7,"path":9},[168],{"id":169,"title":170,"summary":171,"canonicalPath":172,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":173},"high-school-basic-physics-wave-reflection-at-fixed-and-free-ends","固定端・自由端での波の反射","端が動けるかを見て、固定端では上下が反転し、自由端では反転しない反射波を作図します。","\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Freflection-at-fixed-and-free-ends",[17,18,174,175,176],"反射","固定端","自由端",[178],{"id":146,"title":179,"summary":180,"canonicalPath":181,"categoryPath":10,"categoryTitle":18,"difficulty":11,"targetAudience":12,"estimatedMinutes":13,"publishedAt":14,"updatedAt":14,"reviewStatus":15,"tags":182},"音の高さ・大きさ・音色","音の高さ・大きさ・音色を、振動数・振幅・波形へそれぞれ対応させ、音速から波長を求めます。","\u002Fhigh-school\u002Fbasic-physics\u002Fwave\u002Fsound-properties-and-waveform",[17,18,148,183,184],"振動数","音色",[],1785565319584]