A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the
wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the
sculpture?
To solve this problem, we can use the formula for the fundamental frequency of a vibrating string:
f = (1/2L) * sqrt(Tension/mass)
where:
f is the fundamental frequency
L is the length of the wire
Tension is the tension in the wire
mass is the mass of the sculpture
We are given:
L = 90 cm = 0.9 m
f = 80 Hz
First, let's solve for the tension in the wire. We can assume that the tension is equal to the weight of the sculpture. The weight of an object is given by:
Weight = mass * gravity
where gravity is approximately 9.8 m/s^2.
Since we want the tension in Newtons, we need to convert the weight to N:
Weight (N) = mass (kg) * gravity (m/s^2)
Now we can solve for the tension:
Tension = Weight = mass * gravity
Given that the wire hums at its fundamental frequency, we can find the mass of the sculpture by solving for it in the equation:
f = (1/2L) * sqrt(Tension/mass)
Rearranging the equation, we get:
mass = Tension / (f^2 * 4 * L^2)
Substituting the known values, we have:
mass = (Weight / (0.9)^2) / (80^2 * 4)
To find the mass, we need the weight of the sculpture. Unfortunately, the problem statement does not provide the weight or any other information to derive it. If you have access to additional information in the problem statement, please provide it so I can assist you further.