A guitar string has a mass per unit length of 2.45 g/m. If the string is vibrating between points that are 60.0 cm apart, determine the tension F when the string is designed to play a 10.6722 F = note of 110 Hz (A2). Incorrect
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.
![**Problem Statement:**
A guitar string has a mass per unit length of 2.45 g/m.
If the string is vibrating between points that are 60.0 cm apart, determine the tension \( F \) when the string is designed to play a note of 110 Hz (A2).
**Input:**
\[ F = \boxed{10.6722} \, \text{N} \]
**Feedback:**
Incorrect
**Explanation:**
This problem involves determining the tension in a guitar string based on its mass per unit length, vibrating length, and desired frequency. The given solution attempt of 10.6722 N is marked as incorrect.
To solve such a problem, you can use the formula for the fundamental frequency of a vibrating string:
\[ f = \frac{1}{2L} \sqrt{\frac{F}{\mu}} \]
Where:
- \( f \) is the frequency (110 Hz),
- \( L \) is the length of the string in meters (0.60 m),
- \( F \) is the tension in the string,
- \( \mu \) is the mass per unit length in kg/m (0.00245 kg/m).
Solve this equation to find the correct tension \( F \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe496cfb4-14de-4877-8074-43f9c7c49581%2F15e9b80d-ef9b-402c-a3c2-055dc578ee48%2Fnlw02hh_processed.jpeg&w=3840&q=75)
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