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And so there are only two kinds of waves that can exist on this violin string, standing or traveling.
由于这只有两种波,可以存在在这条弦上，驻波或行波。
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The second thing is, just as in the case of the violin string, the wave equation, as posed by Schrodinger, has a plurality of solutions.
第二，就那个小提琴弦而言，波动方程，被薛定谔所提出的，有许多解法。
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All of the sounds are produced by the strings on the instrument and how the bow is pulled across the instrument.
所有声音都是靠乐器上的弦产生的,琴弓在乐器上来回滑动发声
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Would she have imagined that the world famous whatever remembered how many strings were on the lyre on the bench beside the girl on the label of the cigar box he'd stated at in the tool shed at age ten while she, age eleven.
她能想象到这个世界闻名的诸如此类的人,竟然记得当她11岁，他10岁时在工具间里盯着看的,那雪茄盒上的标签上的姑娘身边,长椅上的竖琴有几根弦吗。
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That's why I call them string guys.
这也是我把他们叫做"弦男"的原因
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The strings are now metallic but sixteenth, seventeenth to eighteenth century they would have been made out of cat or sheep gut.
弦现在是金属的,但在十六,十七,到十八世纪,弦是用猫肠或羊肠线制作的
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Let's take the situation where we take a violin string and we pluck it.
让我们设想这样一个情景,我们拿着小提琴的弦拉直它。
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I'll play a melody without vibrato and with vibrato so you can see the difference.
我来演奏一段旋律,分有揉弦和没有揉弦两种表现,这样你们就能听出区别
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The modes of vibration in that string are quantized.
在那条弦上的震动模式是量子化的。
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They've got these two guys on here called Nuttin' But Strings."
节目里有两个男生,叫"万能之弦"
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You know them as harmonics or overtones.
你把它们当做和声或弦外音。
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You can do it on other instruments but on a string instrument it's the difference.
很多乐器都能奏出颤音,但弦乐器上 这种揉弦产生的颤音是不一样的
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Okay. First question: What string technique is being used here?
好,第一个问题是,这里运用了什么弦技巧
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Here is the pitch in--of--a string an octave higher so you can see it this way. As you probably know, if you take a long string and pluck it, it's going to take that long string a long time to pass that sort of cycle, if you will, just one pass through that cycle.
这也是个音高,一个高八度的音弦,你可以这样这样看 你们可能知道,如果你拨动长弦,长弦要经过很长时间,才能完成一个震动周期,如果你想,可以尝试下
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The violin string extends from x equals zero to x equals L, and we pluck the violin string.
弦从X轴指向原点,让x等于L，然后我们拉直那根弦。
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