To determine the frequencies and power of the harmonics of an FM modulated wave, we need to consider the formula for FM modulation and the specific values provided.
The formula for an FM modulated wave can be expressed as:
V_FM(t) = V_c * cos(2πf_c t + β sin(2πf_m t))
Where: V_FM(t) is the FM modulated wave V_c is the amplitude of the carrier wave f_c is the frequency of the carrier wave β is the modulation index f_m is the frequency of the modulating signal
In this case, we have: V_c = 5 f_c = 450k (450,000 Hz) β = 2
To calculate the frequencies of the harmonics, we need to consider the modulation index β. For β = 2, we can expect a significant number of harmonics to be present. The frequency of each harmonic can be calculated using the formula:
f_harmonic = n * f_m
Where: f_harmonic is the frequency of the nth harmonic n is the harmonic number f_m is the frequency of the modulating signal
In this case, we'll calculate the frequencies of the first five harmonics:
For the first harmonic (n = 1): f_harmonic_1 = 1 * f_m = f_m
For the second harmonic (n = 2): f_harmonic_2 = 2 * f_m
For the third harmonic (n = 3): f_harmonic_3 = 3 * f_m
For the fourth harmonic (n = 4): f_harmonic_4 = 4 * f_m
For the fifth harmonic (n = 5): f_harmonic_5 = 5 * f_m
To calculate the power of the harmonics, we need to consider that the power is proportional to the square of the amplitude. Since the amplitudes of the harmonics are not provided, we cannot determine their power without additional information.
Therefore, based on the information given, we can calculate the frequencies of the harmonics but cannot determine their power.