Answer in Physics for jay #254806
January 23rd, 2023
If a cord is under a tension of F T = 135 N, and has a mass per unit length of 0.10 kg/m, what power is
required to transmit a 120-Hz transverse wave of amplitude 2.0 cm?
The power in transverse wave is given as follows (see https://opentextbc.ca/universityphysicsv1openstax/chapter/16-4-energy-and-power-of-a-wave/):
“P = dfrac12mu A^2omega^2v”
where “mu = 0.10kg/m”, “A = 2.0cm = 0.020m”,
“omega = 2pi f”
where “f = 120Hz” and
“v = sqrt{dfrac{F_T}{mu}}”
where “F_T = 135N”. Combining it all together, obtain:
“P = dfrac12mu A^2(2pi f)^2sqrt{dfrac{F_T}{mu}} = 2pi^2mu A^2f^2sqrt{dfrac{F_T}{mu}}\nP = 2pi^2cdot 0.1cdot 0.02^2cdot 120^2cdot sqrt{dfrac{135}{0.1}} approx 4.2times 10^2W”
Answer. “4.2times 10^2W”
