Acoustics from A to Z by Eric E. Ungar
Editor’s Note: We are republishing Eric Ungar’s Acoustics from A to Z from previous NNI issues as part of our initiative to include more educational articles. Their lessons are just as valid today. Look for more in future issues and on noisenewsinternational.net
Nowadays, it is not much of a trick to measure accelerations of 1 milli-g (mg) at 1 kHz. The corresponding displacement amplitude turns out to be of the order of a mere 10-8 inches, which is equal to about 0.0002 micrometers or 2 Ångström units. Compare this to the 40 micrometer typical diameter of a human hair and to the wavelength of visible light, which is in the 4000 to 8000 Ångström range!
It is interesting to explore what happens if I drop an accelerometer onto a floor from a height of 10 cm, for example. If the floor were to cause the accelerometer to decelerate uniformly, making it come to rest within 10-3 cm, then the accelerometer would experience a mere 10,000 g and probably would be damaged. That’s one reason for being careful with accelerometers.
In many vibration situations one observes relatively small accelerations and relatively large displacements at low frequencies. At high frequencies, the situation tends to be reversed. That is why displacement sensors are better at low frequencies and accelerometers are better for measurements at high frequencies. Velocity is often used to characterize or specify vibrations, because it tends to exhibit mid-range magnitudes over larger ranges of frequency. Among the criteria that are stated primarily in terms of velocity are those for judging the quality of rotating machines, for determining the perceptibility of vibrations and for assessing the suitability of a floor for various types of sensitive equipment.
G’s refer acceleration
To our earth’s own gravitation.
Displacements may be very small
For g’s that aren’t small at all.
And so, in many situations,
Velocity’s used to mark vibrations.
The HEARING threshold, it is known,
Is six dB for a pure tone
Precisely at one thousand Hertz,
Agreed upon by most experts.
The smallest pressure we can hear?
A billionth of an atmosphere.
To be precise, according to the American National Standards Institute’s specification for audiometers, the threshold of perception (measured at the ear) of a pure tone at 1 kHz is 6.5 dB relative to the standard 2 × 10-5 Pa. This sound pressure level corresponds to an acoustic pressure of 4.3 × 10-10 atmospheres. The threshold generally is greater at frequencies that deviate from 1 kHz. For example, at 20 Hz the threshold is about 90 dB higher and at 20 kHz it is about 50 dB higher than that at 1 kHz. Although the frequency range of human hearing is generally stated as extending from 20 Hz to 20 kHz, the human ear actually is sensitive to a wider range.[1]
The standard threshold of perception applies to “young persons with no otological irregularities.” As we get older, our hearing sensitivity at frequencies above a few kHz decreases, causing older people to have increasing difficulty distinguishing ‘t’ from ‘p’ and ‘s’ from ‘f’ sounds, for example. Unfortunately, much information content of spoken sounds lies in this range. To quote Bies and Hansen[2], “Old folks may not laugh as readily at jokes, not because of a jaded sense of humor, but rather because they missed the punchline” – I assume they meant due to a hearing loss.
The threshold of pain due to sound in the audio frequency range is about 145 dB, corresponding to a sound pressure of the order of 0.004 atmospheres. In the infrasound range, below 20 Hz, the pain threshold is higher. As discussed by von Gierke and Nixon[3] intense infrasound typically is more felt than heard. It may cause dizziness, coughing, breathing problems and localized pain, but generally has no effect on hearing. Intense ultrasound (above about 17 kHz) can cause headaches, tinnitus (a spontaneous ringing sensation in the ears) and malaise, but its detrimental effect on hearing has not been generally demonstrated. These adverse effects on ultrasound occur only in people who can hear these high -frequency sounds; those of us who are older are safe.
[1] Peter Narins, Professor of Physiological Science at UCLA, took me to task – and rightfully so – regarding the statement I made to the effect that the threshold of hearing corresponds to 6.5 dB. He pointed out that the hearing of about 1.5 million visitors was tested at a Bell Telephone exhibit at the 1938 New York World’s Fair and it was determined that at 1 kHz the average sound pressure to evoke a threshold sensation was 0.0002 dynes per square centimeter. This value has since been used as the standard reference sound pressure, in reference to which the hearing threshold corresponds to 0 dB. This is correct, of course. The 6.5 dB I cited corresponds to the threshold sound pressure measured at the eardrum. The external ear provides amplification, enabling us to perceive at the eardrum a pressure that corresponds to an external sound pressure of 0 dB. (For more details see Chapter 123, “Hearing Thresholds” by W. A. Yost and M. C. Killion, in the Encyclopedia of Acoustics, edited by M. J. Crocker, John Wiley & Sons, Inc., 1997.)
[2] Engineering Noise Control, D. Bies and C. H. Hansen, Unwin Hyman Ltd., 1988.
[3] “Damage Risk Criteria for Hearing and Human Body Vibration,” H. E. von Gierke and C. W. Nixon, Chapter 16 of Noise and Vibration Control Engineering, L. L. Beranek and I. L. Ver, Eds., John Wiley & Sons, Inc. 1992.