### Harmonic Motion in a Stretched String**Problem Statement:**A stretched string fixed at each end has a mass of **47.0 g** and a length of **8.20 m**. The tension in the string is **40.0 N**.**Questions:****(a) Determine the positions of the nodes and antinodes for the third harmonic.** *(Enter your answers from smallest to largest distance from one end of the string.)***Nodes:**- [ ] m- [ ] m- [ ] m- [ ] m**Antinodes:**- [ ] m- [ ] m- [ ] m**(b) What is the vibration frequency for this harmonic?**- [ ] Hz**Explanation:**For a string fixed at both ends, nodes and antinodes are formed at specific positions during harmonic vibrations. Nodes are points where there is no motion, and antinodes are points where the motion is maximum.**Third Harmonic:**In the case of the third harmonic, the string will have three antinodes and four nodes, including the two fixed ends. The positions of these nodes and antinodes are determined based on the length of the string and the harmonic.**Steps to Find the Positions and Frequency:**1. Calculate the position of nodes and antinodes: - For the n-th harmonic of a string of length \(L\), the positions of the nodes are at distances of \( L/n \), \( 2L/n \), ..., \( n-1)L/n \). - The positions of the antinodes are at distances of \( L/(2n) \), \( 3L/(2n) \), ..., \( (2n-1)L/(2n) \).2. Calculate the vibration frequency: - The fundamental frequency \( f_1 \) of a stretched string is given by \( f_1 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \), where \( T \) is the tension and \( \mu \) is the linear mass density (\( \mu = \frac{m}{L} \)). - For the n-th harmonic, the frequency \( f_n = n \times f_1 \).By following these steps, you can determine the required positions for nodes and antinodes, as

A stretched string fixed at each end has a mass of 47.0 g and a length of 8.20 m. The tension in the string is 40.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Enter your answers from smalle to largest distance from one end of the string.) nodes: antinodes: EEEE EEE (b) What is the vibration frequency for this harmonic? Hz

A stretched string fixed at each end has a mass of 47.0 g and a length of 8.20 m. The tension in the string is 40.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Enter your answers from smalle to largest distance from one end of the string.) nodes: antinodes: EEEE EEE (b) What is the vibration frequency for this harmonic? Hz

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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