Updated 12/22/08

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THE ULTRASOUND SPECTRUM



Sound waves with frequencies above those used by humans are called ultrasound. Sounds generated or heard by humans range from above zero to near 20 kHz. The useful range of ultrasound pressure waves is from 20 kHz to roughly 10 MHz. Medical applications, such as ultrasound imaging, are probably the most familiar to the general public. Many insects, rodents, bats, and fish make use of portions of the ultrasound spectrum for feeding, communication, and navigation. Some species use both audio and ultrasound. Except for structural and medical testing, ultrasound use is nil above about 160 kHz for biological use, due to the near total absorption of the wave over short distances through the air. Table 1 notes a brief listing.

Table 1: Ultrasound Frequencies & Users

Band Frequency Range
Users
     
infrasound 0-20 Hz elephants, whales, the earth
audio 20 Hz - 20 kHz humans, insects, animals, fish, sonar
ultrasound 20-30 kHz rodents
ultrasound 20-75 kHz insects
ultrasound 20-160 kHz bats, dolphins
ultrasound 100-2000 kHz structures testing
ultrasound 1 - 10 MHz medical applications
AM radio 0.5 - 1.6 MHz AM radio


Sound pressure levels (SPL) emitted across species, recorded at about a foot, are from about 70 to 110 dB. Signals emitted vary from simple sine waves to complex waveforms with bandwidths and center frequencies as high as 120 kHz. With frequency-divider and frequency shift (direction conversion) receivers, we hear most of this activity as a pattern of clicks.

SPL is defined as follows:

au1eqn1

1 Pa is equal to (perhaps the more familiar) 10^-5 bar (10 μbar). A very strong signal at 110 SPL would represent a pressure of:

au1eqn2

Since the pressure of an acoustic point source is reduced by a factor of 1/r at a distance r, one can say that the signal is reduced 6 dB for each doubling in distance from the source reference point. Hence a 7 times doubling would result in a distance of 128 feet. The resulting signal would be 110 – 6*7 or -68 dB. This is still a strong enough signal to hear in a moderate gain direction conversion receive using a 40 kHz front end and 8-ohm headphones. Adding a parabolic dish to boost gain only adds range as noted below. Since pressure waves at 40 kHz loose about 0.2 dB per foot, long distance communication is uncommon.

The speed of sound in air at 0 deg C is 330 meters/second, or 1,082 ft/sec. In general it is dependent upon the combination of gases making up the media and is a function of temperature, increasing about 0.2% per degree C above 0 deg C. The velocity of sound in air can be calculated from the following:

au1eqn3

where γg is the ratio of the specific heats of the gases at constant pressure and constant volume (1.4), Pa is the ambient pressure (105 n/sq-m), and ρv is the density of the gases (1.29 kg/m3), all at 0 deg C.

Many of the formulas you are likely familiar with for radio projects apply to acoustic projects. For example, the velocity of a wave in a medium is equal to the produce of its frequency and wavelength. Using this equation, we’ve listed the wavelength of several ultrasound signals at different frequencies in Table 2. Note that the wavelength at the popular 40 kHz experimental frequency is just 0.027 feet or about one-third of an inch. Given this fact, it is clear that a one or two foot parabolic dish can be used effectively to boost weak signals in conjunction with a piezo transducer (PZT) receiver. So, you can think of ultrasound kind of like light rather than the usual dimensions for radio projects!

Table 2: Ultrasonic Parameters

Band Freq Velocity wavelength wavelength
  kHz Meters/sec meters feet
audio 1 330 0.3300 1.0827
ultrasound 20 330 0.0165 0.0541
ultrasound 40 330 0.0083 0.0271
ultrasound 120 330 0.0028 0.0090
ultrasound 1000 330 0.0003 0.0011
radio 7000 3E+8 42.8 140.6