Question

Explain the distance that you were no longer able to hear the books drop (or where it was faint)

Answer 1

Short answer: sound level drops about 6 dB for every doubling of distance in free field (inverse‑square law). So the distance where you can no longer hear (or only faintly hear) a dropped book depends on (1) how loud the drop is at a reference distance, (2) the ambient/background noise where you stand, and (3) room acoustics, wind, obstacles and listener hearing.

How to estimate it
1. Measure or estimate the source level. Get the peak sound level of the book drop at a known reference distance (e.g., SPLref = 60 dB at rref = 1 m).
2. Pick an audibility threshold. A practical choice is the ambient noise level where the listener is (if the book’s sound is at or below the background it will be inaudible). For “faint” you might allow the signal a few dB above background.
3. Use the far‑field formula:
SPL(r) = SPLref − 20·log10(r / rref)
Solve for r: r = rref · 10^((SPLref − SPLthreshold)/20).

Example calculations (SPLref = 60 dB at 1 m)
- Quiet bedroom (background ≈ 30 dB): r ≈ 1·10^((60−30)/20) ≈ 31.6 m
- Quiet library (≈ 20 dB): r ≈ 100 m
- Typical office (≈ 50 dB): r ≈ 3.2 m
- Busy street (≈ 60 dB): r ≈ 1 m

Notes and caveats
- The inverse‑square rule applies in the far field and outdoors (or in very large rooms). Close to the source (near field), and inside rooms with reflections, the drop won’t follow the simple 20·log10 rule exactly.
- Frequency matters: higher frequencies attenuate faster in air; low frequencies travel further. A book drop is broadband, so some components can be heard farther than others.
- Background noise usually determines audibility more than the absolute threshold of hearing (0 dB). Human hearing is most sensitive around 2–4 kHz; if the drop’s energy is concentrated there it will be easier to hear at distance.
- To get accurate results: record the drop or use a sound level meter at several distances, measure peak SPL and background SPL, then use the formula or plot the measured decay to find where signal ≈ background.

Practical takeaway: in noisy places you’ll only hear a book fall for a few meters; in a very quiet, open area you might hear it faintly tens of meters away. Exact distance depends on the measured source level and the local ambient noise.