Sound intensity describes how much sound power passes through a certain area each second, so it tells us how strong a sound wave is at a location. It matters in physics, hearing safety, audio engineering, and environmental noise measurement. Because sound energy spreads out as waves travel, intensity usually decreases with distance from the source.
The decibel scale helps us compare very quiet and very loud sounds using numbers that are easier to read.
Key Facts
- Sound intensity is power per area: I = P/A.
- For a point source spreading uniformly, intensity follows the inverse-square law: I = P/(4πr^2).
- Doubling the distance from a point sound source reduces intensity to one-fourth: I2/I1 = (r1/r2)^2.
- Sound level in decibels is β = 10 log10(I/I0), where I0 = 1.0 × 10^-12 W/m^2.
- An increase of 10 dB means the intensity is 10 times larger, while an increase of 20 dB means the intensity is 100 times larger.
- Typical levels are about 0 dB for the threshold of hearing, 60 dB for normal conversation, 90 dB for heavy traffic, and 120 dB near the threshold of pain.
Vocabulary
- Sound intensity
- Sound intensity is the sound power carried by a wave per unit area, measured in watts per square meter.
- Decibel
- A decibel is a logarithmic unit used to compare a sound intensity to a reference intensity.
- Reference intensity
- The reference intensity is I0 = 1.0 × 10^-12 W/m^2, approximately the faintest sound a typical human ear can detect at 1000 Hz.
- Inverse-square law
- The inverse-square law states that intensity from a point source decreases in proportion to the square of the distance from the source.
- Logarithmic scale
- A logarithmic scale represents equal multiplication factors as equal steps, which is useful for quantities with very large ranges.
Common Mistakes to Avoid
- Treating decibels like ordinary linear units is wrong because 80 dB is not twice as intense as 40 dB. Decibels compare intensity ratios using a logarithm.
- Forgetting to square the distance in the inverse-square law gives incorrect intensity changes. If distance doubles, intensity becomes one-fourth, not one-half.
- Using β = 10 log10(I0/I) reverses the ratio and gives the wrong sign. The correct sound level formula is β = 10 log10(I/I0).
- Confusing intensity with loudness can lead to misleading conclusions. Intensity is a physical energy flow, while perceived loudness depends on the ear, frequency, and the listener.
Practice Questions
- 1 A speaker produces sound power of 0.50 W and radiates uniformly in all directions. What is the sound intensity 2.0 m from the speaker? Use I = P/(4πr^2).
- 2 A sound has intensity 1.0 × 10^-6 W/m^2. What is its sound level in decibels using I0 = 1.0 × 10^-12 W/m^2?
- 3 Two students stand at different distances from the same small speaker, one at 1 m and one at 4 m. Explain which student receives greater sound intensity and by what factor, assuming the sound spreads uniformly.