Question

Problem 43

Answer 1

Given information

Given values:

 

The length of the string  

 

The frequency ratio of nearby notes is

 

we are asked to find the position of the first 6 frets, x=?

Step-by-step explanation

Step 1.

A standing wave on a string has a fundamental wavelength when exactly half of a wavelength can fit between the two endpoints of the string. As a result, the fundamental wavelength is as follows:

  

The basic wavelength is , while the string's length is  . Standing waves form after that when the wavelength is:

 

  

 

As a result, the fundamental wavelength divided by equals the -th standing wavelength ( must be a positive integer).

Because the string's tension and mass density remain constant, the wave speed remains constant. For two adjacent notes, the frequency ratio has to be.