Question

一列向右傳播的簡(jiǎn)諧波某時(shí)刻波形如圖10-9-10所示,此時(shí)P點(diǎn)振動(dòng)方向向下,波速v=0.6 m/s,質(zhì)點(diǎn)Q的坐標(biāo)為x_Q=0.90 m.求:

 圖10-9-10

(1)從圖示時(shí)刻起經(jīng)多長(zhǎng)時(shí)間質(zhì)點(diǎn)Q開始振動(dòng)?它開始振動(dòng)時(shí)振動(dòng)方向是怎樣的?

(2)從Q點(diǎn)開始振動(dòng)起經(jīng)多長(zhǎng)時(shí)間質(zhì)點(diǎn)Q第5次到達(dá)波峰?

(3)質(zhì)點(diǎn)Q到達(dá)波峰時(shí),質(zhì)點(diǎn)P在何處?

Answer 1

解析:(1)波動(dòng)過程中波形勻速向右平移,Q點(diǎn)平始振動(dòng)時(shí)間等于PQ的間距與波速的比值,t=(0.90-0.30)/0.6 s=1.0 s;波傳播過程中,后面質(zhì)點(diǎn)是重復(fù)前面質(zhì)點(diǎn)的振動(dòng),故Q點(diǎn)起振時(shí)振動(dòng)方向應(yīng)向下.

    (2)由T=λ/v可求得T=0.4 s,Q點(diǎn)開始振動(dòng)時(shí)運(yùn)動(dòng)方向向下,再經(jīng)T第一次到達(dá)波峰,又經(jīng)4個(gè)周期第5次到達(dá)波峰,總時(shí)間為4.75T=1.9 s.

    (3)由圖可知波長(zhǎng)為0.24 m,PQ之間距離為0.60 m,是波長(zhǎng)的2.5倍,可推得P點(diǎn)與Q點(diǎn)振動(dòng)情況相反,故Q點(diǎn)在波峰時(shí),P點(diǎn)恰在波谷.

答案:(1)1.0 s  向下  (2)1.9 s  (3)波谷