A trend: " The frequency of traffic jams in major cities has almost doubled in the last ten years."

在过去的10年里，大城市的交通拥堵频发率几乎增了两倍。

But for a pipe that’s closed on one end, you can’t double the fundamental frequency, or quadruple it -- or multiply it by any even number.

但是对于一端封闭的管道，您不能将基频加倍或四倍——或乘以任何偶数。

Pythagoras, a Greek philosopher who lived around 500BC, is said to have discovered that notes that sound harmonious together have simple ratios between their frequencies: for example, one that is an octave higher than another has double the frequency.

据说公元前500年左右，希腊哲学家毕达哥拉斯已经发现了发音和谐的音符在频率之间成简单比例：例如，高一个八度的音符具有两倍的频率。