Calculation of Modulation index and Maximum frequency deviation in FM wave

For a FM signal v(t) = 25 cos ( 15* 10⁸t + 10 sin 1550t), calculate

Modulation index
Maximum frequency deviation

Options:

a) 10, 3000.1Hz
b) 20, 1550.9Hz
c) 10, 2465.9Hz
d) 10, 2000.0Hz

Correct Answer: c) 10, 2465.9Hz

Explanation:

Standard expression for FM signal is given by
v(t) = A cos ( ω_ct + mf sin ω_mt)
Comparing with the given equation,
Modulation index m_f = 10
Maximum frequency deviation is given by
m_f = Δf/f_m
Δf = m_f * f_m
Here f_m = 1550/2Π = 246.59 Hz
Δf = 10* 246.59
= 2465.9Hz