How do I calculate the frequencies of the following?

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Homework Help Overview

The discussion revolves around calculating frequencies related to physical systems, specifically a steel wire in a piano and the human ear canal. The subject area includes concepts from wave mechanics and acoustics.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to determine the tension required for a piano wire to produce a specific frequency and the fundamental frequency of the human ear canal. There are questions regarding the appropriate formulas to use for these calculations.

Discussion Status

Some participants have provided numerical attempts for the tension calculation, with one participant suggesting a formula. There appears to be ongoing exploration of the correct values and methods to apply.

Contextual Notes

The problem involves specific measurements and conditions, such as the length and mass of the wire, as well as the dimensions of the ear canal. There may be assumptions regarding the ideal behavior of these systems that are being discussed.

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7. A steel wire in a piano has a length of 0.9000 m and a mass of 4.000 10-3 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC = 261.6 Hz on the chromatic musical scale)?


8. The human ear canal is about 2.6 cm long. If it is regarded as a tube open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive?
 
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Do I use:

f = TM/L√2L
 
For the first one I got T = 49888794.74
 
Oh wait the first one is T = 985 N
 

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