Question

The sixth harmonic of a 70 cm long guitar string has a frequency of 557.14 Hz. What is the velocity of sound in the guitar string?

Answer 1

Answer:

The velocity of sound in the guitar string = 129.99 m/s

Explanation:

Harmonics: A harmonic is a note with frequency equal to an integral multiple of that of the fundamental frequency.

Note: The harmonics of a string is the same as the harmonics of an open pipe.

f₆ = 3v/l ............................ Equation 1

making v the subject of the equation,

v = f₆l/3 ......................... Equation 2

Where f₆ = Is the sixth harmonics of the the string, v = velocity of sound in the guitar string, l = length of the guitar string.

Given: f₆ = 557.14 Hz, l = 70 cm = 0.7 m.

Substituting into equation 2

v = (557.14×0.7)/3

v = 129.99 m/s

Thus the velocity of sound in the guitar string = 129.99 m/s