The key on a piano corresponding to the note of freqency 880Hz is depressed very gently,so that the

题目

The key on a piano corresponding to the note of freqency 880Hz is depressed very gently,so that the hammer does not strike the string,but the damper is lifted and the string is free to vibrate.When the key corresponding to the note of frequency 440Hz is struck firmly,it is found that the 880Hz string also vibrates.Give a brief explanation of this phenomenon.Suppose the 220Hz string had also been free to vibrate.What frequencies,if any,would it have emitted when the 440 Hz key was struck?

答案

高次谐波.固定长度的弦震动产生声音,其有多个本征模,对应波长是弦长度的半整数倍.
频率是整数倍.
基频是220Hz的弦,440Hz,660Hz,880Hz也是其本征频率.然而,对440Hz的弦,220Hz不是其本征频率.