Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S19 / 3 / a

The quoted proton energies are explicitly kinetic. For mean ring radius $\bar{R}=215$ m,Using these expressions rather than setting $\beta =1$ at injection givesThe frequency approaches $c/C$ as energy increases; it is the velocity increase, not a change in the prescribed mean ring circumference, that produces the frequency sweep.

The RF harmonic number is the number of RF cycles per revolution, so $f_{\mathrm{RF}}=h{f}_{\mathrm{rev}}$. For $h=32$,The synchronous phase fixes which phase of that voltage is sampled, not the frequency ratio. For a sine voltage, ${\phi }_s=0$ gives zero net accelerating voltage and describes a stationary ideal-energy condition; an actual energy ramp requires a phase producing the required energy gain. A different phase-origin convention changes that statement about the zero of phase, but not the boxed frequencies.