A transverse wave on a cable is described by the function y(x, t)=2.3cos(4.7x+12t−π/2)y(x, t)=2.3cos(4.7x+12t-π/2), where distance is measured in meters and time in seconds. If the linear mass density of the cable is 0.42 kg/m, what is the average power transmitted by the cable?

P=408.01W

Explanation:

We have the wave function:

 (1)

The average power transmitted by the wave is given by:

    (2)

where E is the energy of the wave, mu is the linear mass density, w is the angular frequency, lambda is the wavelength and A is the amplitude.

The general form of a wave equation can be expressed as:

  (3)

by comparing with the equation (1) we obtain that:

Finally, by replacing in (2) we obtain:

hope this helps!!

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j