Question

(3) a heavy piece of hanging sculpture is suspended by a 101.6 cm long, 5.40 g steel wire. when the wind blows hard, the wire hums at its fundamental frequency of 74.8 hz. what is the mass of the sculpture? 1.36*10^-3 kg

Answer 1

The mass of the sculpture can be determined by using the fundamental frequency of a vibrating wire and the wire's properties, involving calculations to find tension and then mass.

Step-by-step explanation:

To determine the mass of the sculpture using the given fundamental frequency and properties of the steel wire, we should use the equation for the fundamental frequency of a vibrating wire, which is f1 = (1/2L) * sqrt(T/μ), where f1 is the fundamental frequency, L is the length of the wire, T is the tension in the wire, and μ is the linear mass density of the wire.

Here's what we know:

• f1 = 74.8 Hz (fundamental frequency)
• L = 101.6 cm = 1.016 m (length of the wire)
• μ = 5.40 g / 101.6 cm = 0.0531 g/cm = 0.0531 kg/m (linear mass density of the wire)

We are asked to find the mass (m) of the hanging sculpture, which also determines the tension in the wire (T = m*g, where g is the acceleration due to gravity). Rearranging the fundamental frequency equation for tension gives us T = (2 * L * f1)^2 * μ. Once we have the tension, we can find the mass by dividing the tension by the acceleration due to gravity (m = T/g).

By inputting the known values and solving for m, we can find the mass of the sculpture.