In a first experiment, a sinusoidal sound wave is sent through a long tube of air, transporting energy at the average rate of $P_{\text{a}\text{v}\text{g}\text{,}1.}.$ In a second experiment, two other sound waves, identical to the first one, are to be sent simultaneously through the tube with a phase difference $$ of either $0,0\mathrm{.}2$ wavelength, or $0\mathrm{.}5$ wavelength between the waves.

$($a$)$ With only mental calculation, rank those choices of $$ according to the average rate at which the waves will transport energy, greatest first.

$0$ wavelength $>0\mathrm{.}2$ wavelength $>0\mathrm{.}5$ wavelength

$0\mathrm{.}5$ wavelength $>0$ wavelength $>0\mathrm{.}2$ wavelength

$0\mathrm{.}5$ wavelength $>0\mathrm{.}2$ wavelength $>0$ wavelength

$0$ wavelength $>0\mathrm{.}5$ wavelength $>0\mathrm{.}2$ wavelength

$0\mathrm{.}2$ wavelength $>0\mathrm{.}5$ wavelength $>0$ wavelength

$0\mathrm{.}2$ wavelength $>0$ wavelength $>0\mathrm{.}5$ wavelength