We appreciate your visit to A violin string is tuned to 430 Hz fundamental frequency When the violinist puts a finger down on the string one fourth of the string. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The frequency of the violin string when played with a finger positioned one-fourth of the string length from the neck end is 860 Hz.
When a violinist puts a finger down on a string, they effectively shorten the vibrating length of the string, causing it to produce a higher pitch. In this case, the finger is placed one-fourth of the string length from the neck end.
To find the new frequency, we can use the formula:
[tex]\[ f' = \frac{f}{n} \][/tex]
Where:
- [tex]\( f' \)[/tex] = new frequency
- [tex]\( f \)[/tex] = original frequency
- [tex]\( n \)[/tex] = fraction of the string length that the finger is placed from the end
Given that the finger is placed one-fourth of the string length from the neck end ([tex]\( n = \frac{1}{4} \)[/tex]), and the original frequency [tex]\( f = 430 \)[/tex] Hz, we can calculate the new frequency as follows:
[tex]\[ f' = \frac{430}{\frac{1}{4}} \][/tex]
[tex]\[ f' = 430 \times 4 \][/tex]
[tex]\[ f' = 1720 \][/tex]
However, this calculation gives us the frequency of the first harmonic, which is not the fundamental frequency we are seeking. The fundamental frequency is the lowest resonant frequency of the string.
Since we know that the finger placement creates a new node, dividing by 2 will give us the fundamental frequency.
[tex]\[ f_{fundamental} = \frac{1720}{2} \][/tex]
[tex]\[ f_{fundamental} = 860 \, \text{Hz} \][/tex]
Therefore, the frequency of the string when played with a finger positioned one-fourth of the string length from the neck end is 860 Hz.
Thanks for taking the time to read A violin string is tuned to 430 Hz fundamental frequency When the violinist puts a finger down on the string one fourth of the string. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
