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Chapter 5 (Hall)

Chapter 5 (Hall). Sound Intensity and its Measurement. Outline. Amplitude, Energy, and Intensity Sound level and the decibel scale Inverse-square law. Amplitude, energy, and intensity. What is the appropriate physical measure of sound strength or weakness? Several possibilities:

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Chapter 5 (Hall)

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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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