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09:38:51",339459357,[8,9,10,11],"1059Hz","1000Hz","941Hz","889Hz",{"courseId":13,"courseImg":14,"courseName":15},"53e1d2ef4961cca8eea3e23969ad2cb9","https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F03a579384a6dc297c89809b582fcc767.png","默认课程","声源S和接收器R在一条直线上以20m\u002Fs相同的速度沿同一方向运动,设声波的传播速度为340m\u002Fs,声源振动频率为1000Hz,则接收器测得的频率为",[18,23,32,41,51,60,69,78],{"answer":19,"createTime":5,"id":6,"options":20,"question":16,"source":21,"type":22},[],[8,9,10,11],"v1",0,{"answer":24,"createTime":5,"id":25,"options":26,"question":31,"source":21,"type":22},[],339459358,[27,28,29,30],"νS","νS(u+vS)\u002Fu","νS(u-vS)\u002Fu","νSu\u002F(u-vS)","声源的频率为νS,声波在媒质中的传播速度为u.接收器R相对媒质静止,声源S相对于媒质以速度vS向接收器R运动,则接收器R接收到的声波频率为",{"answer":33,"createTime":5,"id":34,"options":35,"question":40,"source":21,"type":22},[],339459359,[36,37,38,39],"847Hz","680Hz","720Hz","640Hz","火车以60m\u002Fs的速度行驶时,在铁路旁与铁路平行的公路上有一汽车在火车后方以20m\u002Fs的速度与火车同向行驶,火车汽笛的频率为800Hz,坐在汽车中的人听到火车鸣笛声的频率为(已知空气中声速为340 m\u002Fs)",{"answer":42,"createTime":43,"id":44,"options":45,"question":50,"source":21,"type":22},[],"2026-05-19 20:29:14",377902552,[46,47,48,49],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F99cf778c9503b16a19f20b3398410d9e.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fb2b93b2626a2a8e38c2a92c3c50be78e.webp\">","0","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F5f0d0e1efd79b63006ca47dd6edef07f.webp\">","若Ω由z=1, \u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fe775861f090ba0459265608deeacebc7.webp\">所围成的闭区域,则\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F2b6ff272d3a6946309acbb132f208eb9.webp\">=( )",{"answer":52,"createTime":43,"id":53,"options":54,"question":59,"source":21,"type":22},[],377902553,[55,56,57,58],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F4c3517e6b113ec38dfb55069e0deff38.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F75737945b12db67a2461542a1db7f7a7.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F8a102e6f4ebe0785b62db3482f02ebff.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F4bfa7d7c75bb09b646a2dfb33f3fad70.webp\">","若Ω由柱面\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F88ff4e6436a76e20bc6f396a7ca0a39e.webp\">及平面z=0, 平面z=a (a>0)和平面y=0所围成,将三重积分化为柱面坐标系下的三次积分:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F8771e27e5702416d29676bab78d393c7.webp\">=( )",{"answer":61,"createTime":43,"id":62,"options":63,"question":68,"source":21,"type":22},[],377902554,[64,65,66,67],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F111d5937ac68fc0194c4ca41ceec8111.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F91335591d46daa915f390adce521edc4.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F8c0fb99eeb993a00093835130c280913.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F06cec39a95256b01528cc94fa100e718.webp\">","若Ω是由球面\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ffcd4e3ce54fe8f94e521621f7e8db04c.webp\">围成的闭区域,则化三重积分为球面坐标系下的三次积分:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F4d98deb839bc0ba0c4cb9cca8da662b6.webp\">=( )",{"answer":70,"createTime":43,"id":71,"options":72,"question":77,"source":21,"type":22},[],377902555,[73,74,75,76],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd6d232aaa4e8d4fc50b64d8a77585bcf.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fafff21b6d2bf1fc415425f1905acc19a.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd1a3d637206553dd6eed621023350a3b.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fff6f8bc188f31a6437a22252b4fc2d31.webp\">","若Ω由\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fdb6cb21cad482e2d07cca3a43968f07b.webp\">与\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1ca52323e54e9e6f2383ddc0df33ae77.webp\">所围成,将三重积分化为柱面坐标系下的三次积分:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fd954092ec1491bc89373a98cf1d48ad0.webp\">=( )",{"answer":79,"createTime":43,"id":80,"options":81,"question":86,"source":21,"type":22},[],377902556,[82,83,84,85],"\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F1b1b46b74b5b20904229ea6d559f32f7.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F0650acb12cd5cb3a0f01c8d12fc19cbb.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ffed8d53640713a4e85bc2e45339e25d6.webp\">","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc951935ff049386e41faf2a01995e9bc.webp\">","若Ω是由\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F0b7cb108e8a2ab0c9dd797fc09c89944.webp\">及 z=2 围成的闭区域,则将三重积分化为柱面坐标系下的三次积分为:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Ffd022eeb2f02fbc49133d8b9540b25b2.webp\">=( )"]