How do I calculate the frequencies of the following?

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To calculate the tension required for a steel piano wire to produce a fundamental frequency of middle C (261.6 Hz), the tension must be approximately 985 N. For the human ear canal, modeled as a tube closed at one end, the fundamental frequency can be determined using the formula f = TM/L√2L. The discussion highlights the calculations involved in determining these frequencies based on physical properties like length and mass. Accurate calculations are essential for understanding sound production in musical instruments and human hearing sensitivity. The conversation emphasizes the importance of applying the correct formulas for precise results.
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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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