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Sound and Light

Sound intensity and the decibel scale

  • 3 things to know
  • A2 4

Overview

Sound intensity and the threshold of hearing, the decibel equation with worked levels, why a logarithmic scale is used, the threshold of pain, and the inverse square law.

What you need to know

Answer each one before you reveal it.

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Key term

What is sound intensity, and what is its unit?

Key term

What is the threshold intensity of human hearing?

Key term

How can a person investigate their own threshold of hearing at 1 kHz?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is sound intensity, and what is its unit?

    Model answer

    Sound intensity is the sound power passing through each square metre at right angles to the direction of travel. Sound intensity is measured in W m⁻².

  2. 2

    What is the threshold intensity of human hearing?

    Model answer

    The threshold intensity I₀ is 1 × 10⁻¹² W m⁻², the quietest 1 kHz sound a typical ear can detect. The threshold intensity is the reference level for the decibel scale.

  3. 3

    How can a person investigate their own threshold of hearing at 1 kHz?

    Model answer

    An audiometer plays a 1 kHz tone through headphones, and the intensity is lowered until the listener just cannot hear it. The test is repeated several times for each ear and a mean taken.

  4. 4

    State the equation for the intensity level of a sound in decibels.

    Model answer

    The intensity level in decibels is 10 log₁₀(I ÷ I₀). The symbol I stands for the intensity, and I₀ is the threshold intensity of 1 × 10⁻¹² W m⁻².

  5. 5

    A sound has an intensity of 1.0 × 10⁻⁶ W m⁻². What is its intensity level?

    Model answer

    The intensity level is 60 dB. The working is 10 log₁₀(1.0 × 10⁻⁶ ÷ 1.0 × 10⁻¹²) = 10 × 6 = 60 dB.

  6. 6

    How is the intensity found from a decibel level?

    Model answer

    The intensity is I₀ multiplied by 10 raised to the power of the decibel level divided by 10. A level of 30 dB gives 1 × 10⁻¹² × 10³ = 1 × 10⁻⁹ W m⁻².

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