Final answer:
The unit for measuring the ratio between measured sound pressure and relative sound pressure using logarithms is the sound pressure level, expressed in decibels (dB). It's distinct from sound intensity level and is particularly used for underwater sounds, where a much higher dB level can be encountered than for sounds in air.
Step-by-step explanation:
The unit that measures the ratio between the measured sound pressure and the relative sound pressure using logarithms is called the sound pressure level. This unit, expressed in decibels (dB), is based on comparing the sound pressure of a given sound to a reference sound pressure, typically set at the threshold of human hearing. The sound pressure level is particularly relevant in contexts such as underwater acoustics, where sound behaves differently than in air.
For example, when measuring ocean noise pollution caused by ships, the sound pressure levels may be reported as high as 200 dB, while the same sound measured as a sound intensity level in air would be less than 140 dB. This example illustrates the significance of the sound pressure level scale in certain applications.
To calculate sound pressure levels in decibels, we use the logarithmic relationship: sound pressure level (Lp) = 20 × log₁₀(P / Pref), where 'P' is the pressure amplitude of the sound and 'Pref' is the reference pressure. The reference intensity is usually 10⁻¹² W/m², which is the quietest sound a person with normal hearing can perceive. Hence, a sound with a measured intensity equal to the reference level is assigned a sound pressure level of 0 dB.