The G string on a guitar is 49 cm long and has a fundamental frequency of 196 Hz. A guitarist can play different notes by pushing the string against various frets, which changes the string's length. The fifth fret from the neck gives C (261.63 Hz); the sixth fret gives Db (277.18 Hz). Part A How far apart are the fifth and sixth frets?
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![**Title: Understanding Guitar Fret Calculations**
**Introduction:**
The G string on a guitar is 49 cm long and has a fundamental frequency of 196 Hz. A guitarist can play different notes by pushing the string against various frets, which changes the string's length. The fifth fret from the neck gives C (261.63 Hz); the sixth fret gives D♭ (277.18 Hz).
**Problem:**
**Part A:**
How far apart are the fifth and sixth frets?
---
**Explanation:**
To determine the distance between the fifth and sixth frets, it is important to understand how the frequency of the vibrating string changes with its length. When a string is pressed against a fret, it effectively shortens the vibrating length of the string, which in turn raises its pitch. The relationship between the frequency and length of the string can be given by the following equation:
\[ f = \frac{v}{2L} \]
where \( f \) is the frequency, \( v \) is the speed of the wave on the string, and \( L \) is the length of the vibrating portion of the string.
By comparing the frequencies at the fifth and sixth frets, we can calculate the corresponding lengths and the distance between those frets.
**Graph/Diagram Explanation:**
No graphs or diagrams are provided in the text.
---
This content serves as an introduction and problem statement for students learning about the relationship between the frequency of a vibrating string and its length, as well as practical applications involving musical instruments such as guitars.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b2b1966-cbdc-46cc-aafa-333a90f3e9b8%2Fe3ba9332-a1bb-45a4-890e-25bb9811d856%2Fof5fuy_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
