Answer:
(a) = 0.22 W
(b) = 0.056 W
Explanation:
given information:
the mass of piano wire, m = 3.00 g = 0.003 kg
tension, F = 25 N
length, l = 80 cm = 0.8 m
frequency, f = 120 Hz
amplitude, A = 1.6 mm = 0.0016 m
(a) the average power carried by the wave,
=
(√μF)ω²A²
where,
ω = 2πf = 2π120 = 754
μ =
=
= 0.00375 kg/m
thus,
=
(√(0.00375)(25))(754)²(0.0016)²
= 0.22 W
(b) What happens to the average power if the wave amplitude is halved.
based on the equation above, we know that the average power is proportional to the square amplitude. therefore
=
= 0.056 W