Answer
The mass of the sculpture is 12 kg
Work Step by Step
We can find the speed of the wave along the wire.
$v = f~\lambda$
$v = (f)~(2L)$
$v = (80~Hz)(2)(0.90~m)$
$v = 144~m/s$
We can find the tension in the wire.
$v = \sqrt{\frac{T}{\mu}}$
$v = \sqrt{\frac{T}{m/L}}$
$T = \frac{v^2~m}{L}$
$T = \frac{(144~m/s)^2(0.0050~kg)}{0.90~m}$
$T = 115.2~N$
The tension in the wire will be equal to the weight of the sculpture. We can find the mass of the sculpture.
$mg = T$
$m = \frac{T}{g}$
$m = \frac{115.2~N}{9.80~m/s^2}$
$m = 12~kg$
The mass of the sculpture is 12 kg
