What term describes the ratio of sound intensity to the threshold of hearing?

The term that describes the ratio of sound intensity to the threshold of hearing is indeed the decibel scale. This scale is a logarithmic way to express the intensity of sound, which allows for a more manageable representation of the wide range of human hearing.

The threshold of hearing is defined as the quietest sound that the average human ear can detect, often set at a standard intensity of ( 10^{-12} ) watts per square meter. The decibel level of a sound is calculated using the formula ( dB = 10 \log_{10} \left(\frac{I}{I_0}\right) ), where ( I ) is the sound intensity being measured and ( I_0 ) is the threshold of hearing. This means that a sound at the threshold of hearing corresponds to 0 dB, and any increase in intensity results in a proportional increase in decibel level.

Using this scale is advantageous because it compresses the wide range of sound intensities into a more manageable format, making it easier to communicate about loudness levels. Consequently, the decibel scale is fundamental in both scientific discussions about sound and in practical applications like audio engineering and hearing assessments.