Loudness
Loudness is how strong a sound seems to a listener; it depends mainly on the amplitude of the sound wave and is compared in decibels.
Definition
Loudness is how strong or soft a sound seems, coming mainly from amplitude, since a drum skin swings farther when hit hard and pushes the air harder, carrying more energy. Sound intensity is measured in decibels on a logarithmic scale, where each increase of $10\ \text{dB}$ means ten times the intensity; a whisper is about $30\ \text{dB}$, normal conversation $60\ \text{dB}$, a rock concert $110\ \text{dB}$, and sounds above about $85\ \text{dB}$ can damage hearing with long exposure. Loudness is the psychological correlate of sound intensity $I$, proportional to the square of pressure amplitude, with sound intensity level $\beta = 10\log_{10}(I/I_0)$ where $I_0 = 10^{-12}\ \text{W/m}^2$, equivalently expressed as sound pressure level $20\log_{10}(p/p_0)$ with $p_0 = 20\ \mu\text{Pa}$; perceived loudness also depends on frequency, since the ear is most sensitive near $3\ \text{kHz}$, which is why A-weighted decibels are used for noise regulation, and roughly a $10\ \text{dB}$ increase is judged as a doubling of loudness.
Example
Tapping a drum lightly makes a soft sound, while hitting it hard makes the same drum loud at the same pitch; a vacuum cleaner at $70\ \text{dB}$ has $10$ times the intensity of a $60\ \text{dB}$ conversation and $10{,}000$ times the intensity of a $30\ \text{dB}$ whisper. A point source radiating $0.5\ \text{W}$ uniformly gives $I = 0.5/(4\pi \times 4) \approx 9.9 \times 10^{-3}\ \text{W/m}^2$ at $2\ \text{m}$, or $\beta \approx 100\ \text{dB}$, and at $20\ \text{m}$ the intensity drops $100$-fold to $80\ \text{dB}$, since every doubling of distance costs $6\ \text{dB}$.
Key Insight
Doubling the number of identical sound sources adds only about $3\ \text{dB}$, so two lawnmowers are not twice as loud as one, since the ear judges loudness on a compressed scale. The decibel scale exists because the ear's dynamic range spans $12$ orders of magnitude, from $10^{-12}$ to $1\ \text{W/m}^2$, and a linear scale would need numbers from $1$ to a trillion, while logarithms compress that range to $0$ through $120$.