When a cello string is bowed, many different modes are excited, not just the lowest-frequency mode, which contributes to the richness of the sound. (a) When the bow is taken away the string continues...

When a cello string is bowed, many different modes are excited, not just the lowest-frequency mode, which contributes to

the richness of the sound.

(a) When the bow is taken away the string continues to vibrate. After some time, only the lowest-frequency mode

remains in motion. Why?

(b) When a cellist bows while lightly touching the midpoint of the string, without pressing the finger down on the

string, the lowest-frequency mode and all modes with odd multiples of that frequency are absent. This changes the

tone markedly and is used to achieve a special musical effect. Explain why the odd harmonics are missing.