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?

Answer: The mass of the sculpture is 11.8kg

Explanation:

Using the equation of fundamental frequency of a taut string.

f = (1/2L) * √ (T/μ) ... (Eqn1)

Where

f = frequency in Hertz = 80Hz

T = Tension in the string = Mg

M represent the mass of the substance (sculpture) = ?

g = 9.8m/s^2

L = Length of the string=90cm=0.9m

μ = mass density = mass of string / Length of string

mass of string = 5g=0.005kg

L=0.9m

μ=0.005/0.9 = 0.0056kg/m

Using (Eqn1)

80 = 1 / (2*0.9) √ (T/0.0056)

144 = √ (T/0.0056)

Square both sides

20736 = T/0.0056

T = 116.12N

Recall that T = Mg

116.12 = M * 9.8

M=116.12/9.8

M = 11.8kg

Therefore the mass of the sculpture is 11.8kg