14.2 Sound Intensity and Sound Level - Physics | OpenStax

Learning Objectives

• Relate amplitude of a wave to loudness and energy of a sound wave.
• Describe the decibel scale for measuring sound intensity.
• Solve problems involving the intensity of a sound wave.
• Describe how humans produce and hear sounds.

Key Terms

• Amplitude
• Decibel
• Hearing
• Loudness
• Pitch
• Sound Intensity
• Sound Intensity Level

Amplitude, Loudness, and Energy of a Sound Wave

• Sound Intensity: Power per unit area carried by a wave.
  • Formula: ( I = \frac{P}{A} ) where ( P ) is power, ( A ) is area.
  • SI Unit: W/m²
• Relationship: Intensity is proportional to the square of the amplitude.
  • Greater pressure amplitude = higher intensity.
• Effect of Medium Density: The denser the medium, the lower the sound intensity.

The Decibel Scale

• Decibel (dB): A logarithmic unit to measure sound intensity level.
  • Formula: ( \beta (dB) = 10 \log_{10}(\frac{I}{I_0}) )
  • ( I_0 ) is reference intensity: ( 10^{-12} W/m² ) (threshold of hearing).
• Intensity Level Calculation: Each factor of 10 in intensity corresponds to an increase of 10 dB.
  • Example: A sound 90 dB is 1000 times as intense as 60 dB._

Solving Sound Wave Intensity Problems

Worked Example 1: Calculate Sound Intensity Level

• Given: Pressure amplitude ( p = 0.656 ) Pa
• Calculate Intensity: ( I = \frac{(p)^2}{2\rho v} )
  • ( \rho = 1.29 ) kg/m³, ( v = 331 ) m/s at 0°C
• Result: ( I = 5.04 \times 10^{-4} W/m² )
• Decibel Level: ( \beta = 87.0 ) dB

Worked Example 2: Change in Intensity Levels

• Given: One sound twice as intense as another.
• Decibel Level Difference: 3 dB increase.

Hearing and Voice

• Sound Production: Air pushed through vocal cords, creating pressure vibrations.
• Pitch Variation: Change tension of vocal cords.
• Hearing Range: Humans: 20 Hz to 20,000 Hz.
  • Dogs: up to 45,000 Hz, Bats and Dolphins: up to 110,000 Hz.
• Ear Anatomy:
  • Outer Ear: Transmits sound to eardrum.
  • Middle Ear: Converts sound to mechanical vibrations.
  • Inner Ear: Converts vibrations to electrical signals sent to brain.

Musical Instruments

• Pitch and Instrument Size: Small instruments produce high-pitch; large ones produce low-pitch.
• Timbre: Unique sound quality of instruments due to frequency and intensity combinations.

Practice Problems

1. Calculate the intensity of a wave with 10 W power and 5 m² area.
2. Calculate sound intensity for a sound wave with 0.90 Pa pressure amplitude.

Check Your Understanding

1. Sound Intensity: Power per unit area carried by a wave.
2. Sound Power: Rate of energy transfer by a sound wave.
3. Loudness: Described by intensity level or decibels.
4. Human Hearing Range: 20 Hz to 20,000 Hz.

References

• R. Nave, Vocal sound production, HyperPhysics.