Q.A FM wave is represented by 10sin[2π×10⁸t+5sin2π×200t ] Determine

Comparing the given wave with the standard FM form $v = V_c\sin(\omega_c t + m_f\sin\omega_m t)$ gives the two frequencies and the modulation index, and the deviation is $m_f f_m$. …

[!TLDR]

Matching to the standard FM equation gives $f_c = 100\ \text{MHz}$, $f_m = 200\ \text{Hz}$, $m_f = 5$ and $\Delta f = 1\ \text{kHz}$.

Compare $10\sin[2\pi\times10^{8}t + 5\sin(2\pi\times200t)]$ with the standard form $v = V_c\sin(\omega_c t + m_f\sin\omega_m t)$.

(a) The carrier term is $2\pi\times10^{8}t$, so $f_c = 10^{8} = 100\ \text{MHz}$; the inner modulating term is $2\pi\times200t$, so $f_m = 200\ \text{Hz}$. …