Both ST1 and ST2 — option (B), as recorded in the supplied key.

This item must be flagged. ST2 is false on standard FM theory, and a candidate reasoning correctly would answer option (C). The keyed option is recorded because it is the key; the correct account follows.

ST1 is certainly true. Angle modulation is a non-linear process, and expanding the FM signal in Bessel functions gives

\(s(t)=A_{c}\sum_{n=-\infty}^{\infty}J_{n}(\beta)\cos\left(\omega_{c}+n\omega_{m}\right)t\)

which contains an infinite number of side-frequency pairs spaced at multiples of the modulating frequency. AM produces exactly one pair. In practice the FM spectrum is truncated where the components fall below about 1% of the unmodulated carrier, giving Carson’s rule \(BW\approx 2\left(\Delta f+f_{m}\right)\), but the theoretical bandwidth is unbounded.

Why ST2 is false. The carrier amplitude in the expansion above is \(A_{c}J_{0}(\beta)\), and \(J_{0}\) is an oscillating function that passes through zero. At those values of the modulation index the carrier component vanishes completely :

These carrier nulls are not a curiosity — they are the classical laboratory method of calibrating frequency deviation. The modulating amplitude is raised until the carrier disappears on a spectrum analyser, and since \(\beta=\Delta f/f_{m}\) is then known exactly, the deviation follows as \(\Delta f=2.405\,f_{m}\) at the first null. The energy is not lost; total power is constant in FM and is simply redistributed into the sidebands.

The underlying principle is what distinguishes FM from AM: \(\sum J_{n}^{2}(\beta)=1\), so the total transmitted power never changes with modulation. Modulation only moves power between the carrier and the sidebands, whereas in AM the carrier is fixed and the sidebands add power on top.

Note on the recorded answer. The answer stored here follows the supplied key. On the standard theory the defensible answer is option (C) — ST1 true, ST2 false.