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Exercise:
The highest string of an electric guitar has a length of lO and a specific mass of msO. The fundamental frequency of this string is fO. abcliste abc Calculate the tension force applied to the string. abc What is the percentage change in the tension force if the frequency is increased to fbO? abcliste

Solution:
abcliste abc At the fundamental frequency the wavelength corresponds to twice the string length: lambda ell The propagation speed of waves on the string is thus v_S lambda f ell f labelv The propagation speed can also be expressed as v_S sqrtfracFm^* labelv From refv and refv it follows for the tension force F m^* leftell fright^ FF labelforce timesmstimesleftlright^timesleftfright^ F approx resultFP abc From refforce it follows that the tension force is proportional to the square of the frequency. The ratio of the new to the old tension force is thus fracF'F ratioF leftfracfbfright^ ratio ratiopP This corresponds to an increase of resultchangeP. abcliste
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Exercise:
The highest string of an electric guitar has a length of lO and a specific mass of msO. The fundamental frequency of this string is fO. abcliste abc Calculate the tension force applied to the string. abc What is the percentage change in the tension force if the frequency is increased to fbO? abcliste

Solution:
abcliste abc At the fundamental frequency the wavelength corresponds to twice the string length: lambda ell The propagation speed of waves on the string is thus v_S lambda f ell f labelv The propagation speed can also be expressed as v_S sqrtfracFm^* labelv From refv and refv it follows for the tension force F m^* leftell fright^ FF labelforce timesmstimesleftlright^timesleftfright^ F approx resultFP abc From refforce it follows that the tension force is proportional to the square of the frequency. The ratio of the new to the old tension force is thus fracF'F ratioF leftfracfbfright^ ratio ratiopP This corresponds to an increase of resultchangeP. abcliste
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Attributes & Decorations
Branches
Mechanical Waves
Tags
frequency, propagation speed, standing wave, tension, wavelength
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link