Using schlieren optics as a tool to see the invisible, we describe a technique of visualizing traveling ultrasonic (28 kHz) sound waves in real time. Suitable for lecture demonstration purposes or as an instructional laboratory experiment, our setup can readily demonstrate the reflection of sound waves from surfaces, diffraction effects around objects, interference, and standing waves. Additionally, the incorporation of color filters provides information such as gradient directions and sound wave phase differences not obtainable with just a white light source. As an example, acoustic standing waves are analyzed.
REFERENCES
REFERENCES
Reference 1, p. 51. Those well-trained in the schlieren arts recognize the sensitivity level of an image by the type of disturbances it reveals. This is seldom done in terms of refractive-index gradients, but rather ranked in terms of the deflection angle, δ, in arcseconds. If one can see the warm air generated by rubbing your hands together, this corresponds to δ being about 5–10 arcseconds.
Reference 1, p. 26. For gases other than air, k may vary roughly from 1 to 15 (×10-4 m3/kg).
Reference 4, pp. 3–4. Schlieren sensitivity is directly proportional to the refractivity constant (Gladstone-Dale coefficient) of the gas. By seeding the air with 0.1 mol % of non-resonant sodium vapor (kNa/ kair ≈ 106), the authors improved the sensitivity of their apparatus by a factor of 1000. However, it appears that they erred in their calculation of sound overpressure in air: an incorrect value for L made their result too low by a factor of 100. This makes the prospect of detecting 1 kHz sound waves in air even worse.
To prevent drifting, it is useful to synchronize the light pulse generator with the transducer's sine wave generator. The Pasco model PI 8587C has a TTL output that can be used as a trigger for the light pulse generator.
Kodak Wratten 2 color filter #29 (red) and #61 (green). These are available from Kodak Cinema & Television (800) 621-3456. The website is motion.kodak.com.
Let the positive y-direction be upward. Then, moving upward, a negative refractive-index gradient would be dn/dy < 0. Moving downward (in the negative y-direction), dy < 0, and thus a negative refractive-index gradient becomes 0. Hence the different colors above and below the object.
12.5″ diameter, 3.12 m focal length, f/10, protected aluminum mirror (originally purchased from Edmund Scientific for $600). The company no longer exists and the closest equivalent is a Techspec Precision Parabolic Mirror available from Edmund Optics, Part No. 32-277-522. When set-up space is limited, we also have an 18″ diameter, 2 m focal length, f/4.3 mirror salvaged from a spectrometer. The longer focal length mirror provides greater schlieren sensitivity, but the latter is a higher quality mirror producing better images. Note that at f/10 or higher, the difference between a spherical and parabolic mirror is insignificant for this application and a smaller diameter mirror can cost an order of magnitude less than a 12″ diameter mirror (currently $2500). Many schlieren videos on youtube.com use 6″ mirrors with excellent images.
Reference 1, pp. 46–48, for a full explanation of coincident and off-axis geometries.
Reference 1, pp. 42–46.
LED Engin LZ4-00CW08 cool white, 1 channel, Standard Star MCPCB. Forward voltage = 14 V and current = 0.7 A.
Pasco model PI 8587C digital function generator and Tektronix Arbitrary Function Generator model AFG 1022 are two options we have used. To secure color schlieren images of the standing wave, the function generator must have an external trigger option. The Tektronix generator also has a phase shift adjustment, an added plus.
Most audio power amplifiers have a flat frequency response (within a decibel or so) up to 100 kHz. The power amp should be able to drive a 20-Ω load with a compliance of ¾ A. We use a McIntosh 30-watt audio amplifier, model MC-30.
Pasco model 8587C digital function generator.
The core of the transformer consists of two C-shaped pieces of ferrite which, when put together make a square. The primary is 10 turns of #18 wire and the secondary is 100 turns of #22 wire. The inductance of the primary is 230 μH w/ secondary open and 16 μH w/ secondary shorted. The operational inductance is such that its impedance is well matched to the 8 Ω output of the amp. The inductance of the secondary is 18.8 mH w/ primary open and 1.8 mH w/ primary shorted. It's operational inductance is around 10 mH. The static capacitance of the transducer is 3550 pF. To resonate at 28 kHz, we want an inductance of 9.1 mH. The inductance of the secondary is a close match for that. The output of the transformer can be as much as 400 Vp-p, but we operate it at approximately 50 Vp-p (the minimum power to secure levitation).
