A guitar string has a mass density of 1.50 grams/meter. If the length of the str

Question

A guitar string has a mass density of 1.50 grams/meter. If the length of the string is 0.700 m, what tension should you put on the string to tune it to an A ( frequency of 440 Hz assume the note is the fundamental frequency of the string - it is.)? (should look like '258 N') A guitar string has a mass density of 1.50 grams/meter. If the length of the string is 0.700 m, what tension should you put on the string to tune it to an A ( frequency of 440 Hz assume the note is the fundamental frequency of the string - it is.)? (should look like '258 N')

Explanation / Answer

For fundamental frequency

Wavelength = 2L = 2 x 0.70 = 1.4 m

Wave speed = wavelength * frequency

v = 1.4 * 440 = 616 m/s

And wave speed on string v = sqrt( T / linear density)

and linear density = 1.50 g / m = 0.0015 kg /m

616 = sqrt(T / 0.0015 )

T = 569.18 N Or 569 N

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