Air and Noise Pollution

Handle noise on the logarithmic decibel scale (add sources by L_total = 10 log Σ10^(L_i/10)), and model air-pollutant dispersion with the Gaussian plume, using stack height and exit velocity to limit ground-level concentration.

Key formulas & points

Skim these first — then read the full notes below.

  • NAAQS for PM10, PM2.5, SO₂, NO₂, CO, O₃ in India
  • Noise limits: residential 55 dB(A) day per CPCB
  • Stack height and exit velocity affect ground-level concentration

Topic details

Introduction

Air and noise pollution are assessed against national standards and controlled at source and by dispersion. Noise is measured on the logarithmic decibel scale referenced to the threshold of hearing, and CPCB sets ambient limits by zone (e.g. 55 dB(A) daytime in residential areas).

Scope in B.Tech and GATE syllabus

Because decibels are logarithmic, noise levels cannot be added arithmetically; combining sources uses the energy-summation formula. Doubling the source energy raises the level by 3 dB, a key fact students must internalise.

Why this topic matters in practice

Air pollution is controlled by limiting emissions and dispersing them; the Gaussian plume model predicts the ground-level concentration downwind of a stack, and raising the stack height or exit velocity increases plume rise and dilutes the pollutant before it reaches ground level.

Key relations & formulas

SPLLp=20log10(pp0)dBSPL L_{p} = 20 log_{10}(\frac{p}{p_{0}}) dB
(p_0 = 20 μPa)

Formulas (Indian textbook notation)

  • Combinedlevels:Ltotal=10log10Σ10(Li10)Combined levels: L_{total} = 10 log_{10} Σ 10^(\frac{L_{i}}{10})

Formulas (Indian textbook notation)

  • GaussianplumeC(x,y,z)forpointsourcedispersionGaussian plume C(x,y,z) for point source dispersion

Notation and sign conventions

Relation 1 —
SPLLp=20log10SPL L_{p} = 20 log_{10}
SPLLp=20log10(pp0)dBSPL L_{p} = 20 log_{10}(\frac{p}{p_{0}}) dB
(p_0 = 20 μPa)
Write this relation with symbols exactly as in Environmental Engineering — SK Garg before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Combined levels: L_{total} = 10 log_{10} Σ 10^

Formulas (Indian textbook notation)

  • Combinedlevels:Ltotal=10log10Σ10(Li10)Combined levels: L_{total} = 10 log_{10} Σ 10^(\frac{L_{i}}{10})
Write this relation with symbols exactly as in Environmental Engineering — SK Garg before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
GaussianplumeCGaussian plume C

Formulas (Indian textbook notation)

  • GaussianplumeC(x,y,z)forpointsourcedispersionGaussian plume C(x,y,z) for point source dispersion
Write this relation with symbols exactly as in Environmental Engineering — SK Garg before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Sound pressure level L_p = 20 log₁₀(p/p_0) compresses the enormous range of audible pressures into a manageable scale; the reference p_0 = 20 μPa is the threshold of hearing. Because it is logarithmic, a 10 dB increase corresponds to a tenfold rise in intensity and is perceived as roughly twice as loud.

Governing relations in practice

Combining noise sources uses L_total = 10 log₁₀ Σ10^(L_i/10) because intensities (not levels) add; two equal sources give only a 3 dB increase, which is why silencing one of many similar sources has limited effect.

Design and analysis considerations

The Gaussian plume model treats emissions as spreading in a normal (bell-shaped) distribution about the plume centreline, widening downwind; the ground-level concentration depends on the emission rate, wind speed, atmospheric stability (dispersion coefficients) and the effective stack height (physical height plus plume rise).

Advanced theory and extensions

National Ambient Air Quality Standards (NAAQS) set limits for PM10, PM2.5, SO₂, NO₂, CO and ozone; control strategies combine cleaner fuels, emission scrubbing and tall stacks that disperse residual emissions to keep ground-level concentrations within these limits.

Assumptions and validity limits

State assumptions explicitly before using any relation for air and noise pollution — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Environmental Engineering (Civil) viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Environmental Engineering (Civil) papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to air and noise pollution.
4. Use equation 1:
SPLLp=20log10SPL L_{p} = 20 log_{10}
.
5. Use equation 2:
Combined levels: L_{total} = 10 log_{10} Σ 10^
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Air and Noise Pollution appears in municipal projects and STPs. In Indian civil curricula this topic is tested because it connects theory to water supply and wastewater.
GATE and semester exams often combine air and noise pollution with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use air and noise pollution?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Adding decibel levels arithmetically instead of by energy summation.
• Forgetting that doubling sources adds only 3 dB.
• Ignoring plume rise (using only physical stack height) in dispersion.
• Confusing PM10 and PM2.5 standards or their health basis.

Quick revision checklist

Before attempting air and noise pollution problems, confirm you can:
1. NAAQS for PM10, PM2.5, SO₂, NO₂, CO, O₃ in India
2. Noise limits: residential 55 dB(A) day per CPCB
3. Stack height and exit velocity affect ground-level concentration
Revise the solved examples in Environmental Engineering — SK Garg and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Combining two noise sources

Problem

Two machines each produce a sound pressure level of 85 dB at a point. What is the combined sound level?

Solution

Using L_total = 10 log₁₀ Σ 10^(L_i/10) = 10 log₁₀(10^(85/10) + 10^(85/10)) = 10 log₁₀(2 × 10^8.5) = 10 × (log₁₀2 + 8.5) = 10 × (0.301 + 8.5) = 88.0 dB. So two equal 85 dB sources combine to 88 dB — an increase of just 3 dB, illustrating the logarithmic nature of the decibel scale.

Conceptual check — Air and Noise Pollution

Problem

In a Environmental Engineering (Civil) semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of air and noise pollution." What should a complete answer include?

Exams & GATE

SK Garg — noise addition and barrier attenuation basics.

📖 Standard books (India)

  • Environmental EngineeringSK Garg

    Read: Syllabus unit

    Water supply and wastewater for civil students