Phase locking between two singing wineglasses
CCoupling between two singing wineglasses
Tal Arane, Ana K. R. Musalem, and Moti Fridman
Dept. of Physics of Complex Systems,Weizmann Institute of Science, Rehovot 76100,Israel (Dated: November 1, 2018)Coupling between two singing wineglasses was obtained and investigated. Rubbing the rim ofone wineglass produce a tone and due to the coupling induces oscillations on the other wineglasses.The needed coupling strength between the wineglasses to induce oscillations as a function of thedetuning was investigated.
PACS numbers: 43.20+g, 62.30+d
A wineglass can be made to ”sing” by gently rubbingits rim with a moist finger. The friction between the fin-ger and the rim of the wineglass causes the wineglass tooscillate, to produce a loud, pure tone [1]. The frequencyof the oscillations depends on the volume of liquid in-side the wineglass, whereby adding liquid increases thefluid pressure that retards the wineglass vibration so asto lower the frequency [2]-[3].Here we investigate how two singing wineglasses canbe coupled to each other. Specifically, we show thatwhen the natural oscillating frequency of each wineglassis comparable to each other, it is relatively easy to in-duce oscillations of the same frequency and phase fromone wineglass to the other. However, when their naturaloscillation frequencies differ, it is more difficult to inducethe oscillations, if at all. Such coupling plays an impor-tant role in many ensembles such as coupled bubbles [4],coupled lasers [5], etc.The experimental arrangement is schematically shownin Fig. 1. Two wineglasses were submerged in a watercontainer, and the oscillating frequency of each wineglasswas obtained by illuminating them with laser beams de-rived from a HeNe laser and detecting the reflected light.In this arrangement the ease of introducing oscillationsfrom one wineglass to the other, i.e, the coupling strengthbetween the wineglasses depends on the distance betweenthem, on the water level in the container and on the dif-ference between the natural oscillation frequencies of thewineglasses (detuning).We began our experiments by measuring the naturalfrequency of each wineglass as a function of volume ofwater inside them. We found, as expected, that the nat-ural oscillating frequency decreases from 700HZ to 450HZas the volume of water inside them increases. Then, weinvestigated the behavior and content of the induced os-cillations as compared to the detuning oscillations, whenthe water level inside each was the same as the other.This was done by rubbing the rim of only one wineglassto produce a natural oscillation frequency with a certainamplitude and measuring the amplitude of the oscillationfrequency that is induced in the other wineglass. Thecoupling strength between the wineglasses correspondsto the ratio of amplitudes of the oscillation frequencies.A representative example of the oscillation frequencies, glass laser mirrormirrordetector detector glass scope BS watercontainerglass
FIG. 1: Experimental arrangement for investigating the cou-pling between two wineglasses. amplitudes and phases for the rubbed wineglass (driv-ing wineglass) and the unrubbed wineglass (driven wine-glass) is shown in Fig 2. As evident, the frequencies andphase of both the driving and induced oscillations areessentially identical. Clearly indicating that frequencylocking and phase locking accrue. −3 Time [sec] A m p li t ude [ V ] FIG. 2: Oscillation frequencies and amplitudes for two cou-pled wineglasses. Dashed curves denote the driving wineglassand solid curves the driven. The level of the water in the con-tainer was 13cm. The distance between the wineglasses was5mm.
In order to determine the influence of distance betweenwineglasses and detuning, we repeated the measurement a r X i v : . [ phy s i c s . pop - ph ] J a n above at different distances and different detuning con-ditions. The results are presented in Figs 3- 5. Figure 3shows the coupling strength as a function of distance be-tween the wineglasses, for different levels of water in thecontainer. As evident, the coupling strength decreasessignificantly as the distance between the wineglasses in-creases. On the other hand, the influence of water levelsof water in the container is not significant. Distance between wineglasses [mm] C oup li ng S t r e ng t h height 11 cmheight 12 cmheight 13 cm FIG. 3: Coupling strength between two wineglasses as a func-tion of the distance between them.
Figure 4 shows the coupling as a function of the detun-ing between them, for a certain level of water in the con-tainer (13cm) and a certain distance between the wine-glasses (25mm). The detuning was achieved by simplyvarying the volume of water inside one of the wineglasses.As evident, the induced frequency amplitude decreases asthe detuning is increased. There is a point of critical de-tuning which indicates that induced oscillations can nolonger be achieved in the driven wineglasses at a certaincoupling strength.
Detuning [Hz ] R a t i o o f a m p li t u d e s Critical detuning
FIG. 4: Ratio of amplitudes of the two wineglasses’ oscilla-tions as a function of detuning between them. The distancebetween the wineglasses was 25 mm , and the water level inthe container was 12 cm . Finally, Fig. 5 shows the critical detuning as a functionof coupling strength, for different levels of water in thecontainer. As evident, when the coupiling strength whichinduce oscillations in the driven wineglass increases, thecritical detuning increases as well. Also, when the level ofwater in the contained increases the slops of the curves in-crease, probably due to changes in the damping strengthwhich depend on the water level in the container C r i t i c a l de t un i ng [ H Z ]
11 cm12 cm13 cmContainer water level
FIG. 5: Critical detuning as a function of coupling strengthfor different water levels in the container.
To conclude, the critical detuning of two wineglassesis directly related to the coupling strength between themand vice versa. For higher coupling strength the criticaldetuning is higher. For large detuning, it is necessaryto increase the coupling strength in order to ensure thatinduced oscillations will accure in the driven wineglass. [1] T. D. Rossing, Wine glasses, bell modes, and LordRayleigh,
Phys. Teacher , 582 (1990).[2] Y. Y. Chen, Why does water change the pitch of a singingwineglass the way it does?, Am. J. Phys. , 1045 (2005).[3] K. W. Chen, C. K. Wang, C. L. Lu and Y. Y. Chen,Variations on a theme by a singing wineglass, Europhys.Lett.
334 (2005). [4] R. Manasseh, A. Nikolovska, A. Ooi, and S. Yoshida,Anisotropy in the sound field generated by a bubble chain,
Journal of Sound and Vibration
807 (2004).[5] M. Fridman, V. Eckhouse, N. Davidson, and A. A.Friesem, Efficient coherent addition of fiber lasers in freespace,
Opt. Lett.32