A tuning fork is mounted on a movable trolley. A microphone connected to an oscilloscope is mounted on another movable trolley. The oscilloscope can be used to plot the graph of sine wave, and thus find the equation of the sound wave detected by the microphone. In case I, both the trolleys are stationary. In case-II, the trolley with the tuning fork moves towards the microphone and the microphone is stationary, In case-III, the trolley with the tuning fork is stationary, but the trolley with microphone moves toward the tuning fork. The person who is making observations was a little careless. He writes 3 correct equations for the detected pressure waves, but forget which wave belongs to which case. The 3 detected pressure waves are:
$\mathrm{A}) {\mathrm{P}}_{\mathrm{A}}={\mathrm{P}}_0\sin \left\{\frac{31\mathrm{\pi }}{20}\mathrm{x}-527\mathrm{\pi t}\right\}$

$\text{ B) }{\mathrm{P}}_{\mathrm{B}}={\mathrm{P}}_0\sin \left\{\frac{8\mathrm{\pi }}{5}\mathrm{x}-512\mathrm{\pi t}\right\}$

$\text{ C) }{\mathrm{P}}_{\mathrm{C}}={\mathrm{P}}_0\sin \left\{\frac{31\mathrm{\pi }}{20}\mathrm{x}-496\mathrm{\pi t}\right\}$