The decibel scale is used to measure sound level, which is closely related to how loud a sound seems to us. It matters in music, audio technology, hearing safety, and everyday life because our ears can detect an enormous range of sound intensities. A whisper, normal conversation, a concert, and a jet engine differ so much in intensity that a simple linear scale would be hard to use.
Decibels make this range manageable by using a logarithmic scale.
Key Facts
- Sound level in decibels is given by β = 10 log10(I / I0), where I0 = 1.0 × 10^-12 W/m^2.
- A 10 dB increase means the sound intensity is 10 times greater.
- A 20 dB increase means the sound intensity is 100 times greater.
- A 3 dB increase means the sound intensity is about doubled.
- Sound intensity decreases with distance from a small source by I ∝ 1 / r^2.
- Long exposure above about 85 dB can damage hearing, and louder sounds become dangerous more quickly.
Vocabulary
- Decibel
- A decibel is a logarithmic unit used to compare a sound intensity to a reference intensity.
- Sound intensity
- Sound intensity is the sound power passing through each square meter of area, measured in watts per square meter.
- Logarithmic scale
- A logarithmic scale increases by equal steps for equal multiplication factors rather than equal additions.
- Threshold of hearing
- The threshold of hearing is the quietest sound a typical human ear can detect, about 1.0 × 10^-12 W/m^2 at 1000 Hz.
- Hearing damage
- Hearing damage is injury to the ear, often from loud sound exposure, that can reduce sensitivity to certain frequencies.
Common Mistakes to Avoid
- Treating decibels as a linear scale is wrong because 80 dB is not twice as intense as 40 dB. Each 10 dB increase multiplies intensity by 10.
- Confusing loudness with intensity is wrong because intensity is a physical measurement while loudness is a human perception. Frequency, hearing sensitivity, and exposure time also affect perceived loudness.
- Adding sound levels like ordinary numbers is wrong because decibels are logarithmic. Two identical 60 dB sources together make about 63 dB, not 120 dB.
- Ignoring exposure time is wrong because hearing risk depends on both sound level and duration. A short loud sound may be less harmful than a slightly quieter sound heard for hours.
Practice Questions
- 1 A sound has an intensity of 1.0 × 10^-8 W/m^2. Using I0 = 1.0 × 10^-12 W/m^2, calculate its sound level in decibels.
- 2 A speaker produces 70 dB at a certain position. If the intensity becomes 100 times greater, what is the new sound level in decibels?
- 3 Two instruments play at the same measured sound level, but one seems more piercing than the other. Explain why decibel level alone may not fully describe perceived loudness.