Final answer:
The bandwidth of the amplitude-modulated signal f(t) is twice the frequency of the message signal. For the phase-modulated signal e(t), the bandwidth is determined using Carson's rule, but specific bandwidth values cannot be calculated without the frequencies B₀ and w₀.
Step-by-step explanation:
The question involves finding the bandwidth of an amplitude-modulated signal and a phase-modulated signal. The message signal m(t) is given as sin B₀t. When this signal is amplitude modulated, it generates f(t) = sin B₀t cos w₀t, which is a product of two sinusoidal functions with different frequencies. The bandwidth of the amplitude modulated signal can be found using the fundamental principle that the bandwidth of an AM signal is twice the frequency of the message signal. For the phase-modulated signal e(t) = cos(w₀t + sinB₀t), the bandwidth is more complex to determine and generally requires the application of Carson's rule. However, since only f(t) and e(t) are provided without the actual values of B₀ and w₀, the exact numerical bandwidth cannot be calculated with the given information.