Final answer:
To calculate the frequency of the hum produced by a hanging sculpture, we need to first determine the tension in the wire by multiplying its mass by gravitational acceleration, and then use it along with the wire's length and linear mass density in the fundamental frequency formula.
Step-by-step explanation:
The frequency of a hanging sculpture resonating at its fundamental frequency can be calculated using the physics of standing waves on a string. Given that the mass of the sculpture is 11 kg and the wire has a linear density of 0.004 kg/m (since 4.0 g equals 0.004 kg), we can figure out the tension in the wire due to the weight (mass times gravity).
The tension (T) is calculated as T = mg = 11 kg × 9.81 m/s2. The fundamental frequency (f) of the wire vibrating can be found using the formula f = (1/2L) √(T/μ), where L is the length of the wire (0.90 m) and μ is the linear mass density (0.004 kg/m). After getting the value of tension and having the length and the mass density of the wire, we can plug these into the formula to calculate the fundamental frequency, which is the frequency of the hum.