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Chapter 5 (Hall)

Sound Intensity and its Measurement

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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.