Question

A guitar string is 80 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 60 cm, and the string is under a tension of 528 N. What is the frequency of the fundamental?

Answer 1

Answer 2

The frequency of the fundamental (first harmonic) of a vibrating string can be calculated using the following formula:

f = (1/2L) * sqrt(T/μ)

where f is the frequency in Hertz, L is the length of the string, T is the tension in Newtons, and μ is the linear mass density of the string in kg/m.

The linear mass density of the string can be calculated by dividing its mass by its length:

μ = m/L

where m is the mass of the string in grams. We need to convert the mass to kilograms before using this formula:

m = 3.6 g = 0.0036 kg

Now we can calculate the linear mass density:

μ = 0.0036 kg / 0.8 m = 0.0045 kg/m

Substituting the given values into the formula for the frequency of the fundamental, we get:

f = (1/2 * 0.6 m) * sqrt(528 N / 0.0045 kg/m)

f ≈ 162.6 Hz

Therefore, the frequency of the fundamental of the guitar string is approximately 162.6 Hz.