### Analyzing the Effects of Tuning a Guitar String on Frequency and WavelengthWhen you adjust the tension of a guitar string by tightening a knob, it results in certain physical changes to the string, which in turn affects the standing wave produced when you strum the string. Let's delve into the specifics with regard to both the frequency and wavelength of the wave on the string.#### (i) What happens to the frequency?**Comparison of Pre-Tuned and Post-Tuned Situations****Conceptual Explanation:**Before tuning, the string has a particular tension which determines the frequency of the standing wave produced. Upon tightening the knob, the tension in the string increases. According to the wave equation for a string, an increase in tension causes the frequency of the wave to increase. This is because the frequency is directly related to the square root of the tension in the string.**Mathematical Explanation:**The frequency \( f \) of the wave on a string is given by:\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]where:- \( L \) is the length of the string (which remains constant)- \( T \) is the tension in the string- \( \mu \) is the mass per unit length of the stringBy increasing the tension \( T \), the frequency \( f \) increases, assuming \( L \) and \( \mu \) are constant.#### (ii) What happens to the wavelength?**Comparison of Pre-Tuned and Post-Tuned Situations****Conceptual Explanation:**Before tuning, the wavelength is determined by the frequency and the wave speed on the string. When you increase the tension, not only does the frequency increase but the wave speed increases too, because the wave speed in a string is dependent on the tension. **Mathematical Explanation:**The wave speed \( v \) on a string is given by:\[ v = \sqrt{\frac{T}{\mu}} \]The wavelength \( \lambda \) of the wave is related to the frequency and the wave speed by the equation:\[ v = f \lambda \]With an increase in tension \( T \), the wave speed \( v \) increases. Since the frequency \( f \) also increases, the wavelength \( \lambda \) remains constant for a specific mode of vibration or harmonic. Hence, tuning the string does not

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You are playing the guitar and tune a string by tightening a knob. Assume this is the only thing changing in the system. After you tune it, you begin to strum the string creating a standing wave on the string. (i) What happens to the frequency? Compare the pre-tuned and post-tuned situations. Explain conceptually and also with equations used this term. (ii) What happens to the wavelength? Compare the pre-tuned and post-tuned situations. Explain conceptually and also with equations used this term.

You are playing the guitar and tune a string by tightening a knob. Assume this is the only thing changing in the system. After you tune it, you begin to strum the string creating a standing wave on the string. (i) What happens to the frequency? Compare the pre-tuned and post-tuned situations. Explain conceptually and also with equations used this term. (ii) What happens to the wavelength? Compare the pre-tuned and post-tuned situations. Explain conceptually and also with equations used this term.

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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