Sound Intensity
Sound intensity is the power carried by a sound wave per unit area perpendicular to the direction of propagation, measured in watts per square metre (W/m²). It quantifies how much acoustic energy passes through a given surface each second and decreases with the square of the distance from a point source — the inverse square law. Sound intensity is the physical basis for the decibel scale and is central to audiology, architectural acoustics, and occupational noise exposure standards.
Key Formula
I = P / (4π r²)
LaTeX: I = \frac{P}{4\pi r^2}
| Symbol | Meaning | Unit |
|---|---|---|
| I | Sound intensity | W/m² |
| P | Acoustic power of the source | W |
| r | Distance from the point source | m |
Worked Example
Problem
A loudspeaker radiates 2 W of acoustic power uniformly in all directions. What is the sound intensity at a distance of 4 m from the speaker?
Solution
Step 1: Identify P = 2 W, r = 4 m. Step 2: Apply the inverse square law: I = P / (4π r²). Step 3: I = 2 / (4π × 16) = 2 / (201.06) ≈ 9.95 × 10⁻³ W/m².
Answer
Sound intensity ≈ 9.95 × 10⁻³ W/m² at 4 m
Typical Sound Intensities and Their Sources
| Source | Intensity (W/m²) | Approx. dB | Effect on Hearing | Distance |
|---|---|---|---|---|
| Threshold of hearing | 1 × 10⁻¹² | 0 dB | Just audible | N/A |
| Rustling leaves | 1 × 10⁻¹¹ | 10 dB | Very quiet | ~1 m |
| Normal conversation | 1 × 10⁻⁶ | 60 dB | Comfortable | ~1 m |
| Busy traffic | 1 × 10⁻³ | 90 dB | Prolonged exposure harmful | ~10 m |
| Rock concert | 1 × 10⁻¹ | 110 dB | Ear damage possible | ~1 m |
| Jet engine | 1 × 10² | 140 dB | Immediate hearing damage | ~30 m |
Interactive Tools
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Related Terms
Decibel
The decibel (dB) is a logarithmic unit used to express the ratio of a measured sound intensity to a reference intensity, typically the threshold of human hearing (I₀ = 10⁻¹² W/m²). Because the human ear responds to sound over an enormous range of intensities (about 10¹² to 1), a logarithmic scale compresses this range into a manageable 0–140 dB scale. The decibel is used extensively in acoustics, telecommunications, electronics, and audio engineering.
Doppler Effect
The Doppler effect is the apparent change in frequency (and thus pitch or colour) of a wave perceived by an observer when the source of the wave and the observer are moving relative to each other. When a source approaches, the observed frequency increases; when it recedes, the frequency decreases. The effect is named after Austrian physicist Christian Doppler (1842) and applies to all wave types including sound, light, and radar, with applications in medical ultrasound, police speed guns, weather radar, and astronomical redshift measurements.
Acoustic Resonance
Acoustic resonance occurs when an object or air column vibrates at its natural frequency in response to an external sound source at that same frequency, resulting in a dramatic amplification of the sound. The phenomenon arises when standing waves are set up within the resonating object, with nodes and antinodes at fixed positions. Acoustic resonance is exploited in all musical instruments — strings, pipes, and percussion — as well as in architectural acoustics, industrial machinery fault detection, and medical imaging.
From Latin "intensus" (stretched, strained) and Old French "intensité". The physical measurement of sound power per unit area was formally defined in the late 19th century alongside the development of acoustic theory.