Answer :
The lowest frequency sound produced by a 0.33-m-long violin string with a mass of 0.89 g and a 45 N tension force is 195.6 Hz. This is calculated using the formula for the fundamental frequency of a string fixed at both ends, which takes into account the string's length, mass, and applied tension.
To determine the lowest frequency sound produced by a vibrating violin string, we can apply the physics of standing waves on a string. The equation for the fundamental frequency (the lowest frequency) of a string fixed at both ends is given by:
f = (1/2L) * √(T/μ),
where f is the fundamental frequency, L is the length of the string, T is the tension force, and μ is the linear mass density of the string.
Given a string that is 0.33 m long and has a mass of 0.89 g (0.00089 kg), we first calculate the linear mass density:
μ = m/L = 0.00089 kg / 0.33 m = 0.0027 kg/m.
With the provided tension of 45 N, we can now calculate the fundamental frequency:
f = (1/2 * 0.33 m) * √(45 N / 0.0027 kg/m) = 1/(0.66 m) * √(16666.67 m²/s²) = 1/(0.66 m) * 129.095 m/s = 195.6 Hz.
Therefore, the lowest frequency sound produced by the vibrating string is 195.6 Hz.
