A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60^o out of phase?

We know that for a wave v = f$\mathrm{\lambda }$,
So, $\mathrm{\lambda }=\frac{\mathrm{u}}{\mathrm{f}}=\frac{360}{500}=0.72\mathrm{m}$
Now as in a wave path difference is related to phase difference by the relation Phase difference
$\mathrm{\Delta \varphi }=\frac{2\mathrm{\pi }}{\mathrm{\lambda }}$ (path difference $∆$x ) 
Here, phase difference
$\mathrm{\Delta \varphi }={60}^{\circ }=(\mathrm{\pi }/180)\times 60=(\mathrm{\pi }/3)\mathrm{rad}$
So path difference
$\mathrm{\Delta x}=\frac{\mathrm{\lambda }}{2\mathrm{\pi }}\left(\mathrm{\Delta \varphi }\right)=\frac{0.72}{2\mathrm{\pi }}\times \frac{\mathrm{\pi }}{3}=0.12\mathrm{m}$