Surface Environment

Noise & Pollution Control

How sound levels in decibels combine logarithmically — adding equal sources, mixing unequal ones, and the 3 dB doubling rule.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Sound level in decibels is a logarithmic measure, so noise sources do not add arithmetically. Doubling the number of equal sources adds about 3 dB; combining unequal levels requires converting each back to intensity, summing, and taking the logarithm again. This governs how machinery noise builds up on a mine bench and how exposure limits are assessed.

The Core Formula Matrix

N

equal sources** of level

L

L_{t o t a l} = L + 10 lo g_{10} N

Two (or more) unequal levels:

L_{t o t a l} = 10 lo g_{10} (1 0^{L_{1} /10} + 1 0^{L_{2} /10} + \dots)

Doubling rule: two equal sources ⇒

+ 10 lo g_{10} 2 \approx + 3 dB

The ‘IIT Traps’

⚠
Decibels don't add arithmetically. $90 + 90 \neq = 180 dB$ ; two equal 90 dB sources give 93 dB.
⚠
Convert to intensity before summing unequal levels, then take $10 lo g_{10}$ — averaging the dB values is wrong.
⚠
Each doubling adds ~3 dB, not 6. Four equal sources are $+ 6$ dB above one.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Two machines each producing

90 dB

operate together. The combined sound level is approximately:

Q2MEDIUM2 Marks · NAT

Two sources of

85 dB

and

88 dB

operate together. The combined level is ______ dB. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

Five identical machines, each

95 dB

, run simultaneously. The total sound level is ______ dB. (Round off to two decimal places.)