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取两个点波源S1,S2发出的两列相干波,参考图7-62,在介质P点各自的振动量分别为
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图 7-62
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合振动便是
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显然,∆P=2kπ时AP=A1+A2为最大,∆P=(2k+1)π时AP=∣A1-A2∣为最小.如果1,2恒定,那么AP的大小由r1,r2确定,即由P点的空间位置确定,出现了干涉现象.波源S1,S2的初相位1,2恒定,确保了AP的大小仅由r1,r2确定,如果1,2经常变化,AP的大小会因受1-2的影响而随时间变化,破坏了干涉现象.在某些波源S1,S2中,虽然1,2会随时间变化,但仍能保持1-2恒定,同样也可产生干涉现象.
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取两列振幅相同的相干平面简谐波,假设分别沿x轴正、负方向传播,即有
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相干叠加后,x处的合振动为
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平移x轴的坐标原点和时间零点,即引入x′和t′,使得
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则
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