Sound Intensity

Overview

Engineering reference data for Sound Intensity in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Symbol	Description	Unit
$c$	Speed of sound	m/s
$L$	Sound level	dB
$\lambda$	Wavelength	m
$f$	Frequency	Hz

Intensity Scale Effects

The relationship between sound intensity factors and corresponding decibel level increases follows a logarithmic pattern:

• Increasing intensity by a factor of *10 raises its level by 10 dB
• Increasing intensity by a factor of *100 raises its level by 20 dB
• Increasing intensity by a factor of *1,000 raises its level by 30 dB
• Increasing intensity by a factor of *10,000 raises its level by 40 dB

Note: Doubling sound pressure raises the sound pressure level by 6 dB.

Loudness Perception

The subjective feeling of loudness corresponds to different sound intensity level ranges:

• 110 to 225 dB: Deafening
• 90 to 100 dB: Very Loud
• 70 to 80 dB: Loud
• 45 to 60 dB: Moderate
• 30 to 40 dB: Faint
• 0 to 20 dB: Very Faint

Distance Relationship

Sound intensity decreases with distance from the source, following the inverse square law. This relationship is expressed as:

$$I = \frac{N}{4 \pi r^2}$$

where:

• $I$ is the sound intensity (W/m²)
• $N$ is the sound power of the source (W)
• $\pi$ is approximately 3.14
• $r$ is the radius or distance from the source (m)

This demonstrates that doubling the distance from a sound source reduces the intensity by a factor of four.

References

• Original Source