Consider a sinusoidal wave on s stretched string in the form y$($x$,$t$)=$Acos$($kx$-$t$).$

Convince yourself that a mass element $$m at $($x$,$t$)$ is undergoing a simple harmonic

oscillation with amplitude A and angular frequency $.$

a$)$ What is the kinetic energy dK of the $$m at $($x$,$t$).$

b$)$ What is the potential energy dU of the $$m at $($x$,$t$).$

c$)$ What is the total mechanic energy dE $=$dK$+$dU on a length of string that is equal to the

wavelength.

d$)$ Convince yourself that the answer you get for $3$c$)$ will be the energy transmitted over

period T$.$ Now get the formula for average power transmission which should be the same

as Shankar $19\mathrm{.}12.$

e$)$ If done correctly, the answer you get for $3$b$)$ for dU will be different from Shankar

$19\mathrm{.}7.$ Neither is necessarily wrong. Please explain the difference