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Understanding Sound Intensity: Measurement, Energy, and the Decibel Scale

This chapter explores sound intensity, its measurement, and the physics behind amplitude and energy. It introduces key concepts such as the relationship between sound intensity and amplitude, illustrating how power is distributed over area. The decibel scale for measuring sound levels is explained, along with the inverse-square law that governs sound propagation. Real-world examples clarify these principles, helping to understand how sound levels are quantitatively compared to a standard intensity. Exercises are included for practice.

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Understanding Sound Intensity: Measurement, Energy, and the Decibel Scale

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  1. Chapter 5 (Hall) Sound Intensity and its Measurement PHY 1071

  2. Outline • Amplitude, Energy, and Intensity • Sound level and the decibel scale • Inverse-square law PHY 1071

  3. Amplitude, energy, and intensity • What is the appropriate physical measure of sound strength or weakness? • Several possibilities: • Pressure amplitude of the sound wave • Energy carried by the sound wave • Intensity PHY 1071

  4. Amplitude • The pressure amplitude of a sound is the greatest variation of pressure above and below atmospheric. A A PHY 1071

  5. Energy • The energy of a sound wave is related to the amplitude. • The energy of an oscillation is proportional to the square of the amplitude. • Example: Consider three different waves called X, Y, and Z. Let Y have twice the amplitude of X, and Z twice the energy of X. Compare the strength of Y and Z. PHY 1071

  6. Power and intensity • Power: The rate of energy transfer; that is, the energy received by the receiver per unit time (1 W = 1 J/s). P = E/t. • Example: A 100 W light bulb, uses 100 joules of energy for each second it stays on. • Intensity: Power per unit area. I = P/S = E/St (W/m2). S is the area of the receiver. • Example: A total power P = 10 W spread evenly over a surface of area S = 5m2. Find the intensity. • Relation between intensity and amplitude: Intensity is proportional to the square of the wave amplitude. • Example: comparing two sound waves’ intensities using a ratio. (I1/I2) = (A1/A2)2. PHY 1071

  7. Sound level and the decibel scale • Measure sound intensity: Use the sound intensity level (SIL) scale, which is labeled in decibels (dB). • Sound level meters that give readouts in decibels. • Compare sound levels: If sound Y carries 10 times as much energy as sound X, we say its level is 10 dB higher, or IY/IX = 10 means SIYY – SIYX =10 dB. • If sound Z carries 100 times as much energy as X, how many decibels higher is the sound level of Z than X? (Answer: IZ/IX = 100 means SILZ – SILX = 20 dB.) PHY 1071

  8. Compare sound intensity level • In general, if I1/I2 = 10n, then SIL1 – SIL2 = 10n dB. • Example: If I1 /I2 = 107, the first sound level is 70 dB higher than the second. • If the ration is not a simple power of 10, use Table 5.1. • Example: Suppose that SIL1 – SIL2 = 36 dB, what is the ratio I1/I2? (Answer 4000). • Example: Suppose that the ratio I1/I2 = 300, What is the level difference SIL1 – SIL2? • Rule: When intensity ratios are multiplied, level difference is dB are added. PHY 1071

  9. Compare all sounds to a certain standard I0 • The standard is a very soft sound. Its intensity I0 = 0.000000000001 W/m2 = 10-12 W/m2. • Other sounds are compared to this standard I0. • Example: A reading on the sound level meter shows 90 dB (a level sometimes attained in musical performance). What is the intensity of this sound? (Answer: 10-3 W/m2) PHY 1071

  10. Table 5.2 PHY 1071

  11. The inverse-square law • Observation: As we move father away from a steady source of sound, we expect the sound level reading to diminish. • Explanation: Sound moves out uniformly in all directions. I2/I1 = (r1/r2)2 – the inverse square-law. • Example: If you measured 84 dB when 10 m from the source, what will be the sound level reading at 20 m, 40 m, and 80 m? (Answer: 78 dB, 72 dB, 66 dB) PHY 1071

  12. Homework • Ch. 5 (Hall), P. 86, Exercises: #1, 2, 3, 5, 6, 7. PHY 1071

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