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I am not a physicist but I am extremely interested in this area.

The simple version of my question is:

"What is the maximum range of an ultrasonic wave traveling through air?" Now, I know it depends on the exact frequency, air temperature, humidity, ... I don't need to know exact number. I just need to know the order of magnitude. Is it ~1m? ~10m? ~1000m?

I also know that this range is finite due to wave's attenuation and attenuation is higher as frequency is higher. So this question could possibly be translated into these two: "What is the minimum ultrasonic wave amplitude detectable by a commercially available sensor?" + "What is the maximum ultrasonic wave amplitude that can be emitted by commercially available ultrasound emitter?"

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A 'ultrasonic' wave can travel arbitrarily far, just like a regular sound wave, it depends on the amplitude of the signal. Regarding your 'two' questions: you'd probably need to look it up... – DilithiumMatrix Jan 26 '13 at 4:18
    
The reason I'm asking this is the following: everytime I see a discussion about measuring distance using ultrasonic waves I see proximity sensors e.g. In cars, in card readers... I am interested in measuring distance in range 1m-100m indoors using ultrasound. Required precision would be +- 5cm. – ancajic Jan 26 '13 at 12:05
up vote 4 down vote accepted

There is a comprehensive article on absorption of ultrasonic waves in air at http://www.ktu.lt/ultra/journal/pdf_50_1/50-2004-Vol.1_09-A.Vladisauskas.pdf.

We're not supposed to just quote links in articles, but it seems silly to reproduce the entire paper here. The conclusions are that absorption is strongly affected by air temperature and pressure (though I'd guess you're only interested in normal pressure) and also by frequency. At low frequencies and temperatures (around zero C) the absorption is very small. However as the temperature increases the absorption rises with temperature. For low frequencies (c. 100KHz) the absorption peaks around 50C at about 5 dB/m. For frequencies around 1MHz the absorption is several hundred dB/m and doesn't show a peak below 100C.

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Thank you for reply. The link is very helpful, but I guess I was hoping for something a little bit more from industry's standpoint. As I said in the comment below the question, everywhere I look, I allways find ultrasonic devices that detect proximity in range of up to ~5m. And I am wondering why hasn't anybody invented an ultrasonic device that would consist of emitter on one side and receiver on over 100m distance that could measure the correct distance without lasers or other stuff? – ancajic Jan 26 '13 at 16:52
    
@ancajic for the distance, the problem is more about: speed of sound do vary depending on pressure, temperature, etc. Even if you could transmit a signal over 100m, you wouldn't be able to deduce any reliable distance. – yota Mar 8 at 15:05

It also depends on the transducer, circuit and signal sequencing that you're using. The sensitivity varies across different devices and signal sequencing significantly alters the ability to envelope the signal.

Medium variables can differ too much over a large area. A small change can result in large reading errors.

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The attenuation of sound in air is a function of frequency - the higher the frequency, the greater the attenuation per unit length.

There is also a natural limit to the amplitude of a sound wave: once the peak pressure is more than twice the ambient pressure, you no longer have a traditional "wave" since air pressure cannot go negative.

Third - "ultrasonic" frequencies start at 20 kHz: the limit of (good) human hearing.

Finally - when the sound pressure of a wave has reduced to 0 dB, one can reasonably say it has become "undetectable"; any number of ambient sound sources would add sufficient noise that it would require extremely senstivite equipment to have any chance of picking up the signal. 0 dB is the "limit of human hearing".

Putting these three things together, one could calculate the distance that a 20.1 kHz signal travels in ordinary air (20°C, 40% relative humidity) when the sound source at the origin has a pressure of 194 dB (the theoretical limit of undistorted sound). We will assume this pressure is measured at a distance of one wavelength (about 1 cm) from the transducer; then we have both the inverse square law and the attenuation law to contend with.

From inverse square law, we lose 6 dB for every doubling in distance. If that was the only mechanism for reducing amplitude, the 194 dB signal would drop to zero in (194/6 ~ 31) doublings of distance, or $2^{31}~\rm{cm}$. That is an enormous distance, so we need to look at the attenuation coefficient instead.

According to the paper that John Rennie already referenced "Absorption of ultrasonic waves in air", A. Vladišauskas, L. Jakevičius, ISSN 1392-2114 ULTRAGARSAS, Nr.1(50). 2004 the attenuation of 50 kHz ultrasound at 20 C and relative humididty of 60% is roughly 1 dB / m

This quickly gives us an absolute upper limit of approximately 200 m for any ultrasound signal transmission. "Real world" conditions will greatly affect the answer.

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