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?

Using fn = (nv)/(2L) and plugging in values as fn = f6 = 557.14 = (6v)/(2*0.7) and solving for v, we get v = 130 m/s.

To find the velocity of sound in the guitar string, we need to use the formula:

Velocity = (Frequency * Wavelength)

Since the problem provides the frequency and length of the guitar string, we can find the wavelength using the formula:

Wavelength = 2 * Length / harmonic number

In this case, the harmonic number is 6.

Let's calculate the wavelength first:

Wavelength = 2 * (70 cm) / 6
= 140 cm / 6
= 23.33 cm

Now that we have the wavelength, we can substitute it into the velocity formula:

Velocity = (Frequency * Wavelength)
= (557.14 Hz) * (23.33 cm)
≈ 12992.36 cm/s

Therefore, the velocity of sound in the guitar string is approximately 12992.36 cm/s.