Final answer:
The modulation index in AM radio is the ratio of the amplitude variation due to the audio signal to the amplitude of the carrier wave. Power efficiency refers to the proportion of total power carried by the information-laden sidebands compared to the carrier. AM generally has lower power efficiency as much of the power resides in the unmodulated carrier.
Step-by-step explanation:
The modulation index for an amplitude-modulated (AM) signal is a measure of the extent to which the amplitude varies with respect to the unmodulated carrier wave. This index is found by taking the ratio of the maximum variation in the signal's amplitude (due to the audio or information signal) to the amplitude of the carrier wave. Power efficiency in the context of AM signals relates to how efficiently the power in the transmitted wave carries the information, which is reflected in the percentage of the total power that is contained within the sidebands as opposed to the carrier wave itself.
In the case of AM radio, the carrier wave's amplitude is modulated by an audio signal without changing the carrier frequency. The carrier wave acts as the base signal onto which the audio information is superimposed. Fourier's theorem suggests that an AM signal consists of a carrier with sidebands that contain the modulated information within a narrow frequency range around the carrier frequency. The power efficiency of AM signals is generally not very high compared to other modulation schemes such as FM (frequency modulation), because a significant portion of the power is used by the carrier rather than the information-carrying sidebands.