Frequency Math Question

Question

A 4-string bass guitar has a string length of 34 inches, and an open E-string vibrates at 41.2 Hz (E1) If the sixth fret is pressed down, the string vibrates at 58.27 Hz (B1b). What is the distance from the bass guitar’s bridge to the sixth fret? Round your answer to the nearest .01 inch.

Answer 1

String length and frequency are inversely proportional. So, we'll set up a proportion to solve this problem using the frequencies' inverses: 1/41.2 and 1/58.27. The inverse proportion equation is:

 

(total string length) / (inverse of total string's frequency) = (length to sixth fret) / (inverse of string's frequency when sixth fret is depressed)

 

34/(1/41.2) = x/(1/58.27)

34(41.2) = 58.27x

1400.8 = 58.27x

24.0398 = x

 

To the nearest 0.01 inch, the length from bridge to the sixth fret is x = 24.04 inches.