A bass guitar string produces a frequency of 460 Hz when plucked with no fingers on any of the frets. The same string is plucked again, with a finger placed halfway between the two ends. What frequency does it produce?
To determine the frequency produced when a bass guitar string is plucked with a finger placed halfway between the two ends, we need to understand the relationship between the vibrating frequency and the length of the string.
The frequency produced by a vibrating string is inversely proportional to its length. This means that when the length of the string is halved, the frequency is doubled, and vice versa.
In the given scenario, when the string is plucked with no fingers on any of the frets, the frequency produced is 460 Hz. When a finger is placed halfway between the two ends, it effectively divides the string into two equal halves.
Since the string is now halved in length, the frequency produced is doubled. Therefore, the frequency produced when this string is plucked with a finger placed halfway between the two ends is 2 * 460 Hz = 920 Hz.