In acoustics, what is the SI-derived unit commonly used to express sound intensity level (loudness) on a logarithmic scale?

Introduction / Context:
Sound can be described physically by its intensity (power per unit area) and perceptually by how loud it seems to the human ear. Because the range of sound intensities we can hear is extremely large, acousticians usually work with a logarithmic scale called sound intensity level or sound pressure level. This question asks for the commonly used SI derived unit for this sound level quantity.

Given Data / Assumptions:

• We are concerned with sound intensity level or loudness as normally measured in practice.
• Sound intensity level is defined using a logarithmic ratio of intensity to a reference value.
• The question refers to the SI context but focuses on the practical unit.
• Candidate units include decibel, newton, hertz and tesla.

Concept / Approach:
Pure physical intensity of sound is measured in watt per square metre (W/m^2). However, to match human hearing and handle the large dynamic range, sound level is defined as L = 10 * log10(I / I0) for intensity or L = 20 * log10(p / p0) for pressure, where I0 and p0 are reference values. The resulting quantity is expressed in bels, and more commonly in decibels (dB), where 1 bel = 10 decibels. Decibel is thus the standard practical unit for sound level in the SI system. Newton is a unit of force, hertz is a unit of frequency and tesla is a unit of magnetic flux density.

Step-by-Step Solution:
Step 1: Recall that sound level is often quoted as, for example, 60 dB, 90 dB or 120 dB. Step 2: Understand that dB stands for decibel, a logarithmic unit derived from the SI system. Step 3: Recognise that decibel is dimensionless but is tied to SI base units through the intensity or pressure ratio definition. Step 4: Note that newton (N) is the SI unit of force, not of sound level. Step 5: Note that hertz (Hz) measures frequency, such as pitch of a sound, not its loudness. Step 6: Note that tesla (T) is the unit of magnetic field strength, unrelated to acoustics.

Verification / Alternative check:
Any standard noise regulation document or sound level meter specification will list readings in decibels, often with weightings such as dB(A) to approximate the ear frequency response. Environmental noise limits, workplace safety recommendations and headphone volume guidelines are all specified in dB. This widespread usage confirms that decibel is the conventional unit for sound intensity level.

Why Other Options Are Wrong:
Newton (N): Measures force (kg·m/s^2), used in mechanics, not for sound loudness.

Hertz (Hz): Measures frequency (cycles per second), relevant to pitch, not to how loud a sound is.

Tesla (T): Measures magnetic flux density in electromagnetism, not an acoustic quantity.

Common Pitfalls:
Students sometimes confuse the physical quantity intensity (W/m^2) with the practical measure of loudness (dB). It is important to distinguish between the base SI unit used in formulas and the logarithmic unit used in real world sound measurement. When a question mentions sound intensity level, loudness ratings or decibel values, decibel (dB) is the correct unit to choose.

Final Answer:
The SI derived unit commonly used for sound intensity level is the decibel (dB).