57. IE •• A violin string is tuned to its fundamental, or first harmonic, frequency.

(a) If a violinist wants a higher frequency by changing only its length, should the string be (1) lengthened, (2) kept the same, or

(3) shortened? Why?

(b) If the string is tuned to 520 Hz and the violinist puts a finger down on the string oneeighth of the string length from the neck end, what is the frequency of the string when the instrument is played this way?