dr. jie zouphy 10711 chapter 5 (hall) sound intensity and its measurement
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Dr. Jie Zou PHY 1071 1
Chapter 5 (Hall)
Sound Intensity and its Measurement
Dr. Jie Zou PHY 1071 2
Outline
Amplitude, Energy, and Intensity Sound level and the decibel scale Inverse-square law
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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
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Amplitude The pressure
amplitude of a sound is the greatest variation of pressure above and below atmospheric.
A
A
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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.
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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.
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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.)
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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.
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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)
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Table 5.2
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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)
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Homework
Ch. 5 (Hall), P. 86, Exercises: #1, 2, 3, 5, 6, 7.