What is the speed of sound and tension in a vibrating harpsichord string?

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SUMMARY

The speed of transverse waves in a harpsichord string of length 1.60 m and linear mass density 25.0 mg/m is calculated to be 1440 m/s at a fundamental frequency of 450.0 Hz. The tension in the string can be determined using the equation v = √(T/μ), where μ is the linear mass density. Additionally, the frequency of the sound wave produced in air, given the speed of sound at room temperature is 340 m/s, must be calculated based on the string's vibration frequency.

PREREQUISITES
  • Understanding of wave mechanics and fundamental frequency
  • Knowledge of linear mass density and its implications in string vibrations
  • Familiarity with the equation relating wave speed, tension, and linear mass density
  • Basic principles of sound waves and their propagation in air
NEXT STEPS
  • Calculate the tension in the harpsichord string using the formula v = √(T/μ)
  • Determine the frequency of the sound wave produced by the vibrating string
  • Explore the relationship between string length, tension, and frequency in string instruments
  • Investigate the effects of temperature on the speed of sound in air
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics and sound, as well as musicians and instrument makers interested in the acoustics of string instruments.

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Homework Statement


A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz.
(a) What is the speed of the transverse string waves?

(b) What is the tension?

(c) What are the wavelength and frequency of the sound wave in air produced by vibration of the string? The speed of sound in air at room temperature is 340 m/s.



Homework Equations



v=2Lfn/n

The Attempt at a Solution


Already used above equation to find the speed, 1440 m/s. Not sure how to find part b or c though
 
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You're missing a relevant equation that relates tension of the string to the speed of a wave and the linear mass density of the string. This is given by

[tex] v = \sqrt{\frac{T}{\mu}}[/tex]

Try working with that and see if you can get the rest.
 
For (c): what must the frequency of the sound be?
 

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