A 12 kg 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. What is the frequency of the hum?

frequency of the hum = 81 Hz

Explanation:

The velocity of the wave is determined by the relation

v = √ (T/miu)

where v = velocity of the wave

T = tension on the string

miu = mass per unit length of the string or linear density = m/L

but here m = 5g = 0.005kg

L = 0.9 m

miu = 0.005/0.9 = 0.00556kg/m

To get the tension on the string we multiply the mass of the sculpture by the acceleration due to gravity, 9.8m/s²

T = 12kg x 9.8m/s² = 117.6 N

hence,

v = √ (117.6/0.00556)

v = 145.43 m/s

But

wavelength = 2L = 2 x 0.9 = 1.8m

Also,

frequency = velocity / wavelength

f = 145.43/1.8 = 80.7967 Hz

The frequency of the hum is 80.8Hz approximately 81Hz