What scale measures loudness based on the intensity level of sound relative to the threshold of hearing?

The decibel scale is the correct answer because it quantifies the intensity of sound relative to a reference level, typically the threshold of hearing. This scale is logarithmic, meaning that an increase of 10 decibels represents a tenfold increase in intensity. The threshold of hearing is set at 0 decibels, providing a baseline for measuring sound intensity. It allows us to express sound levels in a way that aligns with human perception; for example, sounds at 30 decibels are perceived as quieter than sounds at 60 decibels, reflecting a significant difference in intensity.

The other scales mentioned do not focus on loudness in relation to the intensity levels of sound. The frequency scale measures the pitch of sound (how high or low it is), the amplitude scale relates to the maximum extent of a vibration (which contributes to loudness but does not directly express intensity in context), and the power scale deals with the energy output of a sound source rather than its perceived loudness. Therefore, the decibel scale is specifically designed to relate sound intensity to human hearing, making it the appropriate choice for this question.