Question

Suppose the B string on a guitar is 24" long and vibrates with a frequency of about 247 Hz. You place your finger on the 5th fret, which changes the length of the string to 18". Which note do you hear when you play the string D (about 294 Hz) O E (about 329 Hz) OG (about 392 Hz)

Answer 1

To solve this problem it is necessary to apply the related concepts to string vibration. This concept shows the fundamental frequency of a string due to speed and length, that is,

$f = \frac{v}{2L}$

Where

v = Velocity

L = Length

Directly if the speed is maintained the frequency is inversely proportional to the Length:

$f \propto \frac{1}{L}$

Therefore the relationship between two frequencies can be described as

$\frac{f_2}{f_1}=\frac{l_1}{l_2}$

$f_2 = \frac{l_1}{l_2}(f_1)$

Our values are given as,

$l_1 = 24"\\f_1 = 247Hz\\l_2 = 18"$

Therefore the second frequency is

$f_2 = \frac{l_1}{l_2}(f_1)\\f_2 = \frac{24}{18}(247)\\f_2 = 329.33Hz$

The frequency allocation of 329Hz is note E.