The mathematical model for a wave on a tightly stretched wire is

y$($x$,$ t$)=0\mathrm{.}380$ sin

$9$t $3$x $+$

$4$

where x and y are in meters, t is in seconds, and $$ of the wire is $60\mathrm{.}5$ g$/$m$.$

$($a$)$

Calculate the average rate energy is conveyed along the wire $($in W$).$

Apply the equation for the power of a wave. You will need to calculate v$.$ Recall the relationship among v$,$ k$,$ and $.$ From the given wave function, you can find k and $$ if you recast the equation so that it is in standard form. You might find the identity

sin$($A$)=$ sin$($ A$)$

helpful. W

$($b$)$

What is the energy per cycle of the wave $($in J$)?$

The energy per cycle is the energy per wave period, T$,$ so multiply your result from part $($a$)$ by T$.$ You will need to determine T by applying a relationship among v$,$ T$,$ and $.$ J