Ecrit par ✅ Quiz : Equation D Onde
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
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{
"quiz_title": "Equation D Onde",
"quiz_slug": "03_equation_d_onde_quiz",
"quiz_description": "Quiz Edu509 : Equation D Onde",
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"time_value": 0,
"time_type": "minutes"
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"questions": [
{
"question_order": 1,
"question_title": "Quelle est la célérité d’une onde de longueur d’onde \\\\( \\\\lambda = 2{,}0\\\\ \\\\mathrm{m} \\\\) et de fréquence \\\\( f = 5\\\\ \\\\mathrm{Hz} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La célérité se calcule par \\\\( v = \\\\lambda f = 2{,}0 \\\\times 5 = 10\\\\ \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "10 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,4 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2,5 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "7 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Pour une onde décrite par \\\\( y(x, t) = 0{,}04 \\\\cos(20 t - 5 x) \\\\), quelle est l’amplitude ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "L’amplitude est le coefficient devant le cosinus, donc \\\\( 0{,}04\\\\ \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "0,04 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "20 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,2 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Quelle est la période d’une onde de fréquence \\\\( 8\\\\ \\\\mathrm{Hz} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période est \\\\( T = \\\\frac{1}{f} = \\\\frac{1}{8} = 0,125\\\\ \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "0,125 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "8 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,08 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,5 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Pour l’équation \\\\( y(x, t) = 0{,}03 \\\\cos(15 t - 6 x) \\\\), quelle est la valeur du nombre d’onde \\\\( k \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le nombre d’onde \\\\( k \\\\) est le coefficient de \\\\( x \\\\) dans l’argument du cosinus, donc \\\\( 6\\\\ \\\\mathrm{rad/m} \\\\).",
"answers": [
{
"answer_title": "6 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "15 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,03 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "21 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Une onde a une longueur d’onde de \\\\( 0{,}5\\\\ \\\\mathrm{m} \\\\) et une période de \\\\( 0{,}2\\\\ \\\\mathrm{s} \\\\). Quelle est sa célérité ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La célérité est \\\\( v = \\\\frac{\\\\lambda}{T} = \\\\frac{0,5}{0,2} = 2,5\\\\ \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "2,5 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,1 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,25 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "2 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Pour une onde progressive se propageant vers \\\\( +x \\\\), quelle est la forme correcte de l’équation d’onde ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour une propagation vers \\\\( +x \\\\), le signe devant \\\\( kx \\\\) est négatif dans le cosinus.",
"answers": [
{
"answer_title": "\\\\( y(x, t) = A \\\\cos(\\\\omega t - kx + \\\\varphi_0) \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\( y(x, t) = A \\\\cos(\\\\omega t + kx + \\\\varphi_0) \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\( y(x, t) = A \\\\sin(\\\\omega t + kx) \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\( y(x, t) = A \\\\sin(\\\\omega t - kx) \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Une onde a une amplitude de \\\\( 3\\\\ \\\\mathrm{cm} \\\\). Quelle est cette amplitude en mètres ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Pour convertir des centimètres en mètres, on divise par 100 : \\\\( 3\\\\ \\\\mathrm{cm} = 0,03\\\\ \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "0,03 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,003 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "3 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,3 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Pour une onde de longueur d’onde \\\\( 1,2\\\\ \\\\mathrm{m} \\\\), quel est le nombre d’onde \\\\( k \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le nombre d’onde est \\\\( k = \\\\frac{2\\\\pi}{\\\\lambda} = \\\\frac{2\\\\pi}{1,2} = 5,24\\\\ \\\\mathrm{rad/m} \\\\).",
"answers": [
{
"answer_title": "5,24 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,2 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,83 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "2,4 \\\\( \\\\mathrm{rad/m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Une onde a une pulsation \\\\( \\\\omega = 18\\\\ \\\\mathrm{rad/s} \\\\). Quelle est sa période ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La période est \\\\( T = \\\\frac{2\\\\pi}{\\\\omega} = \\\\frac{2\\\\pi}{18} = 0,349\\\\ \\\\mathrm{s} \\\\).",
"answers": [
{
"answer_title": "0,349 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "18 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,056 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "3,14 \\\\( \\\\mathrm{s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Pour l’équation \\\\( y(x, t) = 0{,}05 \\\\cos(20 t - 4 x) \\\\), quelle est l’élongation au point \\\\( x = 2\\\\ \\\\mathrm{m} \\\\) à \\\\( t = 0,5\\\\ \\\\mathrm{s} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Argument : \\\\( 20 \\\\times 0,5 - 4 \\\\times 2 = 2 \\\\). \\\\( \\\\cos(2) \\\\approx -0,416 \\\\). Donc \\\\( y = 0,05 \\\\times (-0,416) = -0,0208\\\\ \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "-0,0208 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,0208 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,05 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "-0,05 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Quelle est la fréquence d’une onde de période \\\\( 0,25\\\\ \\\\mathrm{s} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La fréquence est \\\\( f = \\\\frac{1}{T} = \\\\frac{1}{0,25} = 4\\\\ \\\\mathrm{Hz} \\\\).",
"answers": [
{
"answer_title": "4 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,25 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2,5 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,04 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Une onde a une amplitude de \\\\( 0,02\\\\ \\\\mathrm{m} \\\\), une longueur d’onde de \\\\( 0,8\\\\ \\\\mathrm{m} \\\\), une fréquence de \\\\( 5\\\\ \\\\mathrm{Hz} \\\\), et se propage vers \\\\( +x \\\\). Quelle est la pulsation \\\\( \\\\omega \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation est \\\\( \\\\omega = 2\\\\pi f = 2\\\\pi \\\\times 5 = 31,42\\\\ \\\\mathrm{rad/s} \\\\).",
"answers": [
{
"answer_title": "31,42 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "6,28 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,8 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "5 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Quelle(s) affirmation(s) est/sont vraie(s) concernant une onde mécanique ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Une onde mécanique transporte de l’énergie sans transporter de matière et nécessite un milieu matériel.",
"answers": [
{
"answer_title": "Elle transporte de l’énergie sans transporter de matière.",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Elle nécessite un milieu matériel pour se propager.",
"is_correct": true,
"answer_order": 2
},
{
"answer_title": "Elle transporte la matière du point d’émission au point de réception.",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "Elle peut se propager dans le vide.",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Pour une onde de fréquence \\\\( 6\\\\ \\\\mathrm{Hz} \\\\) et longueur d’onde \\\\( 0,7\\\\ \\\\mathrm{m} \\\\), quelle est la célérité ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La célérité est \\\\( v = \\\\lambda f = 0,7 \\\\times 6 = 4,2\\\\ \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "4,2 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,116 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,42 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "7,6 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Quelle est la longueur d’onde d’une onde de célérité \\\\( 8\\\\ \\\\mathrm{m/s} \\\\) et de fréquence \\\\( 2\\\\ \\\\mathrm{Hz} \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La longueur d’onde est \\\\( \\\\lambda = \\\\frac{v}{f} = \\\\frac{8}{2} = 4\\\\ \\\\mathrm{m} \\\\).",
"answers": [
{
"answer_title": "4 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "16 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,25 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "6 \\\\( \\\\mathrm{m} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Pour une onde de période \\\\( 0,5\\\\ \\\\mathrm{s} \\\\), quelle est la pulsation \\\\( \\\\omega \\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation est \\\\( \\\\omega = \\\\frac{2\\\\pi}{T} = \\\\frac{2\\\\pi}{0,5} = 12,57\\\\ \\\\mathrm{rad/s} \\\\).",
"answers": [
{
"answer_title": "12,57 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "3,14 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "6,28 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,5 \\\\( \\\\mathrm{rad/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Une onde a pour équation \\\\( y(x, t) = 0,06 \\\\cos(10 t - 2 x) \\\\). Quelle est la fréquence de cette onde ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La pulsation \\\\( \\\\omega = 10\\\\ \\\\mathrm{rad/s} \\\\), donc \\\\( f = \\\\frac{\\\\omega}{2\\\\pi} = \\\\frac{10}{2\\\\pi} = 1,59\\\\ \\\\mathrm{Hz} \\\\).",
"answers": [
{
"answer_title": "1,59 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "10 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "0,16 \\\\( \\\\mathrm{Hz} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Pour une onde de longueur d’onde \\\\( 2\\\\ \\\\mathrm{m} \\\\) et de période \\\\( 0,25\\\\ \\\\mathrm{s} \\\\), quelle est la célérité ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La célérité est \\\\( v = \\\\frac{\\\\lambda}{T} = \\\\frac{2}{0,25} = 8\\\\ \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "8 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,125 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,5 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "4 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Quelle(s) grandeur(s) physique(s) détermine(nt) la forme d’une onde progressive ?",
"question_type": "multiple_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La forme d’une onde progressive dépend de l’amplitude, de la longueur d’onde et de la fréquence.",
"answers": [
{
"answer_title": "Amplitude",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "Longueur d’onde",
"is_correct": true,
"answer_order": 2
},
{
"answer_title": "Fréquence",
"is_correct": true,
"answer_order": 3
},
{
"answer_title": "Masse du milieu",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Pour une onde de fréquence \\\\( 10\\\\ \\\\mathrm{Hz} \\\\) et de longueur d’onde \\\\( 0,3\\\\ \\\\mathrm{m} \\\\), quelle est la célérité ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La célérité est \\\\( v = \\\\lambda f = 0,3 \\\\times 10 = 3\\\\ \\\\mathrm{m/s} \\\\).",
"answers": [
{
"answer_title": "3 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0,03 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,3 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "30 \\\\( \\\\mathrm{m/s} \\\\)",
"is_correct": false,
"answer_order": 4
}
]
}
]
}