At left is a Simpson Model 886-2 sound level meter, and at right is a General Radio Type 1551-C sound level meter. These are general purpose sound level meters, with which you can demonstrate the measurement of sound intensity. You can use a camera connected to the data projector to display the readout to the class. Alternatively, although this will not provide a readout calibrated in dB, each meter has an output jack, which provides an electrical signal that corresponds to the sound received by the microphone. Connecting this to the voltmeter (on the AC Volts setting) with the large display allows you to show the relative amplitude of the sound in volts.
Whether for the purpose of measuring a person’s aural acuity, designing audio equipment, or measuring ambient noise in a workplace to ensure safety, it is useful to be able to define and measure the intensity of a sound wave. Sound is a longitudinal mechanical wave created by a disturbance in an elastic medium, most commonly air. It is a series of alternating compressions, regions of higher-than-average pressure, and rarefactions, regions of lower-than-average pressure. As the wave travels through the air, these produce pressure fluctuations above and below atmospheric pressure, which we hear as sound. At a reference frequency of 1,000 Hz, the human ear can detect pressure fluctuations as small as about 2 × 10-5 Pa (above and below atmospheric pressure). This is known as the threshold of hearing. On average, atmospheric pressure at sea level is 1.013 × 105 Pa, so this represents a relative change in pressure of about ±1 part in 5,000,000,000. The loudest sound that the ear can receive without pain corresponds to a pressure fluctuation of about 30 Pa, or about ±1 part in 3,400, or over 1,000,000 times greater than the smallest detectable pressure fluctuation. This represents a range of greater than six orders of magnitude over which the ear can detect pressure fluctuations in a sound wave.
The intensity of a wave is defined as the time average rate at which energy is transported by the wave per unit area across a surface perpendicular to the direction in which the wave propagates. Its units are W/m2. The intensity is proportional to the square of the amplitude of the wave, and thus the square of the maximum pressure fluctuation. The smallest audible pressure fluctuation, about 2 × 10-5 Pa, corresponds to a power of 10-12 W/m2, and the pressure fluctuation at the threshold of pain, 30 Pa, corresponds to a power of 1 W/m2. We see that the six-order-of-magnitude range of sensitivity to the pressure fluctuation corresponds to a range of twelve orders of magnitude in power of the sound waves that the ear can detect.
As you might imagine, the ear’s response to sound intensity over this wide range is not linear, but rather it is logarithmic. We perceive changes in the intensity of sounds by equal ratios as equal changes in loudness. That is, if we are exposed to sounds whose intensities differ by a common multiplier, we hear the changes in intensity from one to the next as equal changes in loudness. It makes sense, then, to use some kind of logarithmic scale to express sound levels. Proabably the most commonly used scale is the sound intensity level (SIL) scale. The fundamental unit of this scale is the bel, after Alexander Graham Bell, and is defined by the relation:
SIL = SIL0 + log (I/I0),
where I0 is the intensity of a reference tone in W/m2, and SIL0 is the sound intensity level of the reference tone in bels. Because the bel is a rather large unit, it is not commonly used. Instead, in most cases, people use the decibel, dB, which equals one-tenth of a bel, or:
SIL = SIL0 + 10 log (I/I0),
where, I0 is the intensity of a reference tone in W/m2, and SIL0 is the sound intensity level of the reference tone in decibels (dB). As noted above, the faintest sound that the human ear can detect corresponds to a pressure fluctuation of about 2 × 10-5 Pa, and a power of 10-12 W/m2. This provides the zero reference for the SIL scale. That is, we set the intensity level of 10-12 W/m2 equal to 0 dB, so that
SIL = 10 log (I/I0),
Where I0, the reference intensity, equals 10-12 W/m2. (So 10 log (I/I0) = 10 log (1), and SIL = 0 dB.) For the loudest audible sound, just at the threshold of pain, the intensity is 1 W/m2. The SIL at this level, then, is 10 log (1 W/m2/10-12 W/m2) = 10 log (1012) = 120 dB.
If we double the intensity of a sound of intensity I, whose SIL is, say, N dB, the new SIL is 10 log (2I/I0), or N dB + 10 log (2) dB, or N dB + 3 dB. We see that doubling the intensity of a sound results in an increase in the SIL of 3 dB. Similarly, tripling the intensity of a sound increases the SIL by 5 dB, quintupling it increases the SIL by 7 dB, increasing it by a factor of 10 increases the SIL by 10 dB, increasing it by a factor of 100 increases the SIL by 20 dB, etc. Generally speaking, if we add identical sound sources, or increase the intensity of a single source, in order for the sound to appear twice as loud, we must increase the original intensity by a factor of 10, or increase the SIL by 10 dB.
The table below shows some typical values for a variety of background noises as quoted from a survey by the New York City Noise Abatement Commission in Young, Hugh D. and Geller, Robert M. Sears & Zemansky’s College Physics (San Francisco: Addison Wesley, 2007) p. 388.
Type of Noise Sound Intensity Level, dB Intensity, W/m2 Rock concert 140 100 Threshold of pain 120 1 Riveter 95 3.2 × 10-3 Elevated train 90 10-3 Busy street traffic 70 10-5 Ordinary conversation 65 3.2 × 10-6 Quiet automobile 50 10-7 Quiet radio in home 40 10-8 Average whisper 20 10-10 Rustle of leaves 10 10-11 Threshold of hearing 0 10-12 It bears noting that the SIL scale is an objective scale. That is, it is based on a measurable property of the sound wave – the fluctuation in pressure associated with it. As noted above, the zero reference of the SIL scale is set at the threshold of hearing at the reference frequency of 1,000 Hz. The response of the ear over the entire frequency range of its sensitivity, however, is not flat. That is, compared to a 1,000-Hz tone at a particular SIL, a second tone at the same SIL, but of a different frequency, may appear to be louder or softer than the 1,000-Hz tone. A loudness level scale or phon scale, for which the unit is the phon, accounts for this nonuniform response of the ear. One phon is the loudness level of a pure 1,000-Hz tone whose SIL is 1 dB; 1 phon equals 1 dB at a frequency of 1,000 Hz. For a tone of a different frequency, the loudness in phons equals the SIL of a 1,000-Hz tone that is perceived to be equally as loud.
Operation of the Sound Level Meters
Both of the instruments shown above have virtually identical controls. Each has the following settings:
Speed of Response: This is not labeled, except for the choices, on the Simpson meter, and is labeled “METER” on the General Radio instrument. The choices are “Fast” and “Slow.” On the slow setting, the instruments are less responsive to transient noises.
Range: On the Simpson instrument, the choices are OSHA and settings at 10-dB intervals, ranging from 130 to 50. The meter has two scales. On the OSHA setting, the red scale reads the SIL directly. On the other settings, one reads the black scale, and adds the reading to the setting value to get the SIL. For example, if the setting is 80 dB and the meter reading is +7 dB, the SIL is 87 dB. On the General Radio instrument, the choices are settings at 10-dB intervals, from 140 to 30. The 130-dB setting is also the setting used for calibration (vide infra). To read the SIL, one reads the scale (there is only one) and adds the reading to the setting value, just as for the Simpson meter.
Weighting: As noted above, the response of the ear is not flat over the frequency range in which it is sensitive. For low-intensity-level sounds, as the frequency decreases from 1,000 Hz, the threshold of hearing rises. As the frequency increases from 1,000 Hz, the threshold of hearing dips, and then rises again. This deviation from a flat response is greatest for sounds at low sound intensity levels. As the levels of sound intensity increase, these deviations become less severe, and although the response curve never actually becomes flat, it becomes nearly so for sound intensity levels of about 100 dB. (After this, the deviations toward lower frequency rise a bit.) To account for the average response of the human ear at different sound levels, the American National Standards Committee devised three weighting curves – “A,” “B” and “C.” Guidelines and requirements (for safety monitoring) vary, but typically, Curve A is used for sound levels from about 24 to 55 dB, curve B is used for levels of about 55 to 85 dB, and curve C is for levels from 85 to 140 dB. Both instruments have settings for these three weighting curves. The 20 kc position on the General Radio meter is for use with an analyzer or recorder.
Battery: On the Simpson meter, pressing the button labeled “BATT TEST” shows whether or not the battery (9 V) needs replacing. On the General Radio meter, turning the switch to “1” or “2” under “FIL,” under “BATT TEST,” checks the two D cells that supply current to the tube filaments. (It is a vacuum tube instrument.) Switching to “PL” checks the 67.5-V battery (an Exell 416) that supplies the plate voltage.
Cal: The General Radio instrument has a calibration setting. To calibrate the meter, set the range switch to “130 dB/CAL,” and the weighting switch to “CAL.” Pressing with your thumb or a finger, turn the round black knob in the center, near the meter, so that the needle sits within the region labeled “CAL.”
The Occupational Safety and Health Administration has set standards regarding the maximum level of noise to which workers may be exposed. These are specified in https://www.osha.gov/laws-regs/regulations/standardnumber/1910/1910.95.
Permissible Noise Exposure Limits
For compliance, exposure to impulsive or impact noise must not exceed 140 dB peak sound pressure level.References:
1) Berg, Richard E. and Stork, David G. The Physics of Sound (Englewood Cliffs New Jersey: Prentice-Hall, Inc., 1982) pp.143-8.
2) Young, Hugh D. and Geller, Robert M. Sears & Zemansky’s College Physics (San Francisco: Addison Wesley, 2007) pp. 386-9.
3) Sears, Francis W. and Zemansky, Mark W. College Physics, Third Edition (Reading, Massachusetts: Addison-Wesley, 1960) pp. 433-4.
4) http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/loud.html