The average power transmitted by string wave is given by the expression [tex]P=\frac{1}{2} \mu\omega^2A^2v[/tex], Where μ is a linear density of a string, ω is angular frequency of the wave, A is an amplitude of the wave, v is a speed of wave.
Since [tex]y(x,t)= A sin (kx+\omega t-\psi )[/tex] comparing with [tex]y_1 = 0.12 sin \frac{\pi}{3}(5x+200t-1)[/tex]
A = 0.12 m, ω = [tex]\frac{200\pi }{3} s^{-1}[/tex], k = [tex]\frac{5\pi }{3} m^{-1}[/tex]
Speed of wave, [tex]v = \frac{\omega }{k} = \frac{\frac{200\pi }{3}}{\frac{5\pi }{3} } =40m/s[/tex]
So power [tex]P = \frac{1}{2} *0.02*(\frac{200\pi }{3} )^2*0.12^2*40=253 W[/tex]
