Question

一根彈性繩沿x軸方向放置，左端在原點(diǎn)O處，用手握住繩的左端使其沿y軸方向做周期為1s的簡(jiǎn)諧運(yùn)動(dòng)，于是在繩上形成一簡(jiǎn)諧波．繩上質(zhì)點(diǎn)N的平衡位置為x=5m，振動(dòng)傳播到質(zhì)點(diǎn)M時(shí)的波形如圖所示．                                                                                                                                                  

求：（1）繩的左端振動(dòng)后經(jīng)過多長(zhǎng)時(shí)間傳播到質(zhì)點(diǎn)N；                                                       

（2）質(zhì)點(diǎn)N開始振動(dòng)時(shí)，繩的左端已通過的路程；                                                       

（3）如果從N開始振動(dòng)計(jì)時(shí)，畫出質(zhì)點(diǎn)N振動(dòng)的位移﹣時(shí)間圖線．                                                               

                                                                                       

                                                                                                                                       

Answer 1

（1）由圖可知，波長(zhǎng) λ=2m，則波速：v==m/s=2m/s

振動(dòng)從O傳播到質(zhì)點(diǎn)N經(jīng)歷的時(shí)間：t==s=2.5s

（2）因 n===2.5，所以質(zhì)點(diǎn)N開始振動(dòng)時(shí)，繩的左端已通過的路程為：

 s=2.5×4A=2.5×4×8cm=80cm

（3）由上可知，經(jīng)2.5s波傳播到N點(diǎn)，由波形圖知各質(zhì)點(diǎn)的起振方向向下，振幅為8cm，周期與波的周期相同即T=1s，所以質(zhì)點(diǎn)N的振動(dòng)圖象如圖所示：

答：

（1）繩的左端振動(dòng)經(jīng)2.5s時(shí)間傳播到質(zhì)點(diǎn)N；

（2）質(zhì)點(diǎn)N開始振動(dòng)時(shí)，繩的左端已通過的路程為80cm．

（3）如果從N開始振動(dòng)計(jì)時(shí)，質(zhì)點(diǎn)N振動(dòng)的位移﹣時(shí)間圖線如圖所示．