To determine the second overtone (third harmonic) that can cause a standing wave pattern on a string, we need to use the formula for the fundamental frequency of a vibrating string:
f = (1/2L) * sqrt(T/μ)
where: f is the frequency of the harmonic (in Hz), L is the length of the string (in meters), T is the tension in the string (in N), μ is the linear mass density of the string (mass per unit length, in kg/m).
Given: Length of the string (L) = 67.7 cm = 0.677 m Mass per length (μ) = 1.5 g/m = 0.0015 kg/m Tension (T) = 57.7 N
Using the formula, we can calculate the fundamental frequency (first harmonic) of the string:
f1 = (1/2L) * sqrt(T/μ) = (1 / (2 * 0.677)) * sqrt(57.7 / 0.0015) ≈ 161.94 Hz
The frequency of the second overtone (third harmonic) is three times the frequency of the fundamental frequency. Therefore:
f3 = 3 * f1 ≈ 3 * 161.94 Hz ≈ 485.82 Hz
So, the second overtone (third harmonic) that can cause a standing wave pattern on the given string is approximately 485.82 Hz.