Answer to Question #254806 in Physics for jay

Question

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?

Answer 1

The power in transverse wave is given as follows (see https://opentextbc.ca/universityphysicsv1openstax/chapter/16-4-energy-and-power-of-a-wave/):

$$P = \dfrac12\mu A^2\omega^2v$$

where $\mu = 0.10kg/m$, $A = 2.0cm = 0.020m$,

$$\omega = 2\pi f$$

where $f = 120Hz$ and

$$v = \sqrt{\dfrac{F_T}{\mu}}$$

where $F_T = 135N$. Combining it all together, obtain:

$$P = \dfrac12\mu A^2(2\pi f)^2\sqrt{\dfrac{F_T}{\mu}} = 2\pi^2\mu A^2f^2\sqrt{\dfrac{F_T}{\mu}}\\ P = 2\pi^2\cdot 0.1\cdot 0.02^2\cdot 120^2\cdot \sqrt{\dfrac{135}{0.1}} \approx 4.2\times 10^2W$$

Answer. $4.2\times 10^2W$