If a vibrating string is made shorter (as by holding a finger on it), how does this affect the frequency of...

Question

vibration and pitch???

Answer 1

The string will vilbrate at a higher frequency, and at a higher pitch. think of a guitar.

Answer 2

Frequency is inversely related to length; if you halve the length you double the frequency and get a pitch one octave higher.

In the 12-tone scale of Western music, it's a lucky coincidence that dividing an octave by twelfth roots of 2 (1.059463, 1.122462, etc) results in frequencies that closely match the classic ratios of small whole numbers discovered by Pythagoras and found to be pleasing to the ear.

The roots-of-two ratios are not always an exact match to the whole number ratios, but they are so close that we can't hear the difference. The big advantage to this is that when an instrument is tuned in this "well-tempered" manner, one can change keys and the tune will sound the same only differently pitched.

Starting from any note, the whole-number ratios are 16/15, 9/8, 6/5, 5/4, 4/3, sqrt(2) (halfway, called the tritone), 3/2, 8/5, 5/3, 16/9, 15/8 and 2/1. Compare these with the roots of two.

Answer 3

Pitch and frequency are more or less the same thing - high pitch = high frequency.

The freqency of vibration of a string f = 1/length (L) so as length decreases the frequency increases.