The Ripple Tank – Pt. 5

Published On: June 30, 2023Tags: , , , , , , ,

This week we continue our Ripple Tank series with another snippet of an important thesis paper, one that launched the career path of ASC founder, president and TubeTrap inventor, Art Noxon, PE Acoustical

Operational Constraints  

The water wave system whose depth is less than 1/4 in. provides a frequency independent wave speed, thereby meeting the constant wave speed ratio requirement for the sound wave analogy. The range of applications of this very shallow water system is limited to the ordinary ripple tank experiments which demonstrate two dimensional wave interference and reflection characteristics due to single and multiple point sources.

One dimensional wave situations such as acoustic waves inside a pipe require that the pipe diameter be less than 1/4 wavelength. Similarly, entire Helmholtz apparatus must be within the 1/4 wavelength limit. The wavelength at 12.5 Hz in water 1/4 in. deep is 0.58 in. Therefore its 1/4 wavelength is too small to be physically practical due to excessive surface tension and viscosity effects, which cause great damping of wave action and distortions of the image on the viewing screen. The minimum channel width for satisfactory pipeline wave action is 1/4 in., which corresponds to a minimum wave length of 1 in. A comparative plot of wavelengths (Figure 8) and frequencies for different water depths shows an increasing available frequency range with increasing depth. Advantages of increased water depth are limited by increasing nonlinearity of wave speed changes. The compromise depth of 1 in. provides satisfactory experimental data while offering a relatively broad working frequency band of 1.5 to 15.0 Hz whose upper frequency 1/4 wavelength is 1/4 in while the water depth is within limits of the empirical wave speed equation.

Analog Equations  

Establishment of the 1 inch operating depth criterion allows development of a frequency conversion factor chart whose value depends on the applied water wave frequency, standard speed of sound in air, and the water wave speed. This factor is multiplied by the geometric ratio between the air and water systems to obtain the equivalent acoustic frequency. A plot of this factor (F) is found in Appendix A, page 69.

Equation (3) can be rewritten in terms of factor F:

An alternative to the frequency conversion factor approach in the determination of the equivalent acoustic frequency is to determine the equivalent acoustic wave length.

By using:the scaling equation can be rearranged to show the equivalent acoustic wavelength to be a function of the geometric ratio and the real water wavelength.

This wavelength relationship is independent of water and acoustic wave speeds and is good for any water depth. The only handicap is that the analogy is in terms of wavelengths rather than frequencies, meaning that the water wavelength must be determined for each analogous data point. If the wavelength analogy is employed, a section of the wave tank will have to be devoted to a standing wave fixture which, upon adjustment, will provide the wavelength of any applied frequency. A graph of real wavelengths and associated frequencies for the standard 1 in. water depth is also in Appendix A, page 69.  (shown above)

The Ripple Tank paper concludes! Link to full thesis paper by ASC president and TubeTrap inventor, Art Noxon, PE Acoustical Channel Filter Networks The uniform channel of infinite length is frequency indiscriminate. However, if its impedance at some point is abruptly changed, part of the input power is reflected back upstream. If two or more discontinuities occur within a few wavelengths of each other, the reflected waves interact with the discontinuities and the oncoming wave train to create the effect of wavelength-sensitive chokes and passes to the flow of power down the tube. Filter Resonator The filter network behavior is readily demonstrated by arranging a long channel wave guide with an approximate 2 in. space about midway as illustrated in Figure 18. A variety of discontinuities can be positioned in the space. The wave drive is located at one end of the channel and the other end is left open. Resonance Characteristics A plot of the author's subjective estimate of transmitted power passed through various filter networks at corresponding wavelengths is in Figures 19 through 23. They show the ripple tank system to be wavelength sensitive through the third harmonic due to inertance as well as compliance discontinuities and also to the lower frequency Helmholtz type of resonances. The higher harmonic frequency selectivity and Helmholtz resonance capabilities of the ripple tank carry the analogy to acoustic wave beyond the limitations that plague the systems of electrical analog (Kinsler and Frey, 1950). A channel which is normally 1 in. wide with a 50% enlarged section 2 in. in length has the power attenuation characteristics of Figure 19. The initial low frequency partial choke (H) is a Helmholtz resonance due to the discrete compliant value of the enlarged volume. There is a full choke at the first harmonic, a full pass with the second harmonic and a partial choke of the third while higher frequencies freely pass. This is equivalent to an acoustic pipeline whose diameter is abruptly enlarged over a section of known length. The electrical analog to this is a capacitor shunted across a transmission line, which has no Helmholtz-type reaction, no second harmonic pass and chokes instead of passes upper harmonic frequencies (Kinsler and Frey, 1950) A 2 in. long filter section in the middle of an otherwise uniform channel of 1 in. width is an abrupt 50% reduction in width which produces the power attenuation curve of Figure 20. There is a full choke at the first harmonic and full pass at the second with a partial choke for the third and higher harmonics. This is equivalent to an acoustic pipeline whose diameter is abruptly reduced for a section of its length. The electric analog for this is an inductance placed in series with the transmission line (Kinsler and Frey, 1950), which does not produce the second harmonic pass. The abrupt discontinuities that produce the power attenuation curve of Figure 21 are two sets of walls perpendicular to the wave direction, each of which presents a 50% area reduction. A combination of the filtering effects of the previous two examples is observed. A low-frequency Helmholtz choke is due to the entrapped volume between the pair of walls. A full choke occurs with the first harmonic resonance of the filter section and a full pass with its second. There is a partial choke with third harmonic and higher wavelengths. This is equivalent to installing a pair of ported baffles in an acoustic pipeline. Elimination of compliance for a 2 in. section of the water wave channel is accomplished by eliminating its free surface. A short section of 1 in. square pipe set into the filter section of the water wave channel provides the power attenuation curve of Figure 22. There is a first harmonic full choke, a full pass for the second harmonic, and a full choke of the third and above. Because the compliance area does not equal the inertial area, there is no acoustic analog to this experiment. Changing the value of inertance while retaining the value of compliance of the water wave channel is accomplished by increasing its underwater wall width. The underwater width is increased 50% and the free surface width is unchanged by the filter element which produces the power attenuation curve of Figure 23, There is a full choke with the first harmonic and a full pass with the second. There is a partial choke at the third harmonic wavelength and full pass for anything above. Because the compliance area does not equal the inertial area there is no acoustic analog to this experiment. Future Investigations The behavior of the wave channel filter networks is directly analogous to that noted in comparable acoustic systems (Kinsler and Frey, 1950:225). The size of a filter system consisting of side branch resonator tubes as compared with the size of an equivalent frequency sensitive Helmholtz system is a particular illustration of the required size difference between the two systems. The analogy of the ripple system might well be applied to the design of acoustic mufflers as well as speaking tubes in which engine noises are to be damped and the voice frequencies are passed. Frequency selective ear plugs constitute such systems. Two Dimensional Analogy Consideration of two dimensional wave system analogy is not included in this paper as it is readily available (French, 1966).

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