A guitar string is 90cm long and has a mass of 3.8g. The distance from the bridg

Question

A guitar string is 90cm long and has a mass of 3.8g. The distance from the bridge to the support post is L=62cm and the string is under a tension of 530N.
What are the frequencies of the fundamental and 1st two overtones? A guitar string is 90cm long and has a mass of 3.8g. The distance from the bridge to the support post is L=62cm and the string is under a tension of 530N.
What are the frequencies of the fundamental and 1st two overtones?
What are the frequencies of the fundamental and 1st two overtones?

Explanation / Answer

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fundamental frequency f = (1/2L)(sqrt(T/u)

where u is mass per unit length

so

f = ( 1/2*0.62) *(sqrt(530/(0.0038/0.9)

f   = 285.7 Hz   or 286 Hz

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frequency of 1st over tone = 2f1 = 2*286 = 571 Hz

f3 = 3f 1 = 3*286 = 858 Hz
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