Question
Asked Dec 6, 2019
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How far, and in what direction, should a cellist move her finger to adjust a string's tone from an out-of-tune 449 Hz to an in-tune 440 Hz?  The spring is 68.0 cm long, and the finger is 20.0 cm from the nut for the 449 Hz tone.

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Expert Answer

Step 1

Wavelength and length from end of string to the point of finger is,

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2 = 2(L-L) 2(68cm – 20 cm) = 96 cm

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Step 2

Since speed of wave is constant, 

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(449 Hz)(96cm)= (440HZ)2, 2 =97.9 cm

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Step 3

Length corresponding to wav...

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= 2L, 97.9 cm = 48.9 cm

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