Enter values to see results
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W/m²
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dB SIL
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dB SPL
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m²
Enter values to see results
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W/m²
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dB SIL
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dB SPL
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m²
The Sound Intensity Calculator determines the acoustic intensity at a given distance from a point source radiating into free space. Sound intensity, measured in watts per square meter, represents the acoustic power passing through a unit area perpendicular to the direction of propagation. This calculator applies the inverse-square law, which governs how sound energy spreads over distance, and converts the result to decibel levels for practical comparison.
A point source radiating omnidirectionally distributes its acoustic power uniformly over the surface of an expanding sphere. The intensity at distance $$r$$ is:
$$I = \frac{P}{4\pi r^2}$$
where $$P$$ is the total acoustic power in watts, and $$4\pi r^2$$ is the surface area of a sphere with radius $$r$$.
The intensity level in decibels relative to the standard reference intensity $$I_0 = 10^{-12}$$ W/m² is:
$$L_I = 10 \cdot \log_{10}\left(\frac{I}{I_0}\right) \text{ dB SIL}$$
Under free-field conditions (no reflections), the sound intensity level (SIL) is numerically equal to the sound pressure level (SPL), because the reference values are chosen to be consistent: $$I_0 = 10^{-12}$$ W/m² corresponds to a pressure of $$p_0 = 20 \times 10^{-6}$$ Pa in air at standard conditions.
The inverse-square law predicts that intensity decreases by a factor of 4 (or -6 dB) each time the distance doubles. This is the fundamental principle behind sound level predictions in outdoor acoustics and noise assessment.
At 5 meters from a 0.01 W source, the intensity is about 3.18 × 10⁻⁵ W/m², corresponding to roughly 75 dB — similar to normal conversation at close range. Doubling the distance to 10 m reduces this to about 69 dB (a drop of 6 dB). Human speech has an acoustic power of roughly 10–50 μW, while a symphony orchestra at full volume produces about 1–10 W, and a jet engine can output 10,000 W or more.
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I = 0.01/(4π × 25) = 3.18 × 10⁻⁵ W/m². Level = 10 × log₁₀(3.18 × 10⁻⁵/10⁻¹²) ≈ 75 dB. Comparable to a conversation at arm's length.
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I = 100/(4π × 400) = 0.0199 W/m². Level ≈ 103 dB. This is a high level — hearing protection is recommended for prolonged exposure above 85 dB.
The inverse-square law states that intensity is inversely proportional to the square of the distance from a point source: $$I \propto 1/r^2$$. Doubling the distance reduces intensity by a factor of 4 (or 6 dB). This applies to any quantity that spreads uniformly from a point source, including light and gravity.
Sound intensity is a vector quantity measuring power per unit area (W/m²), while sound pressure is a scalar measuring local pressure fluctuations (Pa). They are related by $$I = p^2/(\rho c)$$ where $$\rho c$$ is the specific acoustic impedance of the medium (approximately 413 rayl for air).
Only approximately in the near field close to the source. Indoors, reflections from walls create a reverberant field where sound level remains relatively constant regardless of distance. The transition between the direct field (inverse-square) and reverberant field occurs at the critical distance.
Normal conversation produces about 10–50 microwatts (μW) of acoustic power. Shouting can reach about 1–2 milliwatts. Even these tiny powers create audible sound levels because the human ear is extraordinarily sensitive, detecting intensities as low as 10⁻¹² W/m².
When distance doubles from $$r$$ to $$2r$$, intensity drops by a factor of $$(2r)^2/r^2 = 4$$. In decibels: $$10 \cdot \log_{10}(1/4) = -6.02$$ dB. This 6 dB rule is a fundamental tool in acoustic engineering for estimating sound levels at different distances.
Directional sources concentrate energy in certain directions, described by a directivity factor $$Q$$. The modified formula becomes $$I = QP/(4\pi r^2)$$. For example, a source on a flat ground (hemispherical radiation) has Q = 2, increasing intensity by 3 dB compared to free-field radiation.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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