Dr. Jie ZouPHY Chapter 5 (Hall) Sound Intensity and its Measurement

Dr. Jie ZouPHY Outline Amplitude, Energy, and Intensity Sound level and the decibel scale Inverse-square law

Dr. Jie ZouPHY 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

Dr. Jie ZouPHY Amplitude The pressure amplitude of a sound is the greatest variation of pressure above and below atmospheric. A A

Dr. Jie ZouPHY 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.

Dr. Jie ZouPHY 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/m 2 ). S is the area of the receiver. Example: A total power P = 10 W spread evenly over a surface of area S = 5m 2. 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. (I 1 /I 2 ) = (A 1 /A 2 ) 2.

Dr. Jie ZouPHY 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 I Y /I X = 10 means SIY Y – SIY X =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: I Z /I X = 100 means SIL Z – SIL X = 20 dB.)

Dr. Jie ZouPHY Compare sound intensity level In general, if I 1 /I 2 = 10 n, then SIL 1 – SIL 2 = 10n dB. Example: If I 1 /I 2 = 10 7, 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 SIL 1 – SIL 2 = 36 dB, what is the ratio I 1 /I 2 ? (Answer 4000). Example: Suppose that the ratio I 1 /I 2 = 300, What is the level difference SIL 1 – SIL 2 ? Rule: When intensity ratios are multiplied, level difference is dB are added.

Dr. Jie ZouPHY Compare all sounds to a certain standard I 0 The standard is a very soft sound. Its intensity I 0 = W/m 2 = W/m 2. Other sounds are compared to this standard I 0. 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: W/m 2 )

Dr. Jie ZouPHY Table 5.2

Dr. Jie ZouPHY 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. I 2 /I 1 = (r 1 /r 2 ) 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)

Dr. Jie ZouPHY Homework Ch. 5 (Hall), P. 86, Exercises: #1, 2, 3, 5, 6, 7.