DO YOU HEAR THE SEA FROM A SHELL?

Verovnik Ivo, National Education Institute of Slovenia, Ljubljana, Slovenia

Mathelitsch Leopold, Institut für Theoretische Physik, Universität Graz, Austria

The talk presented at the First International Girep Seminar: Developing Formal Thinking in Physics, Udine – Italy, September 2001.
This work was supported by the European project Socrates-Comenius, COMEUPHYS 2000.

Abstract

Experiments are proposed how to analyse the resonating sound of hollow bodies like bottles, tubes or sea shells. The necessary software is introduced, the background of the physical phenomena is explained and the implementation in school-physics is discussed.

Holding a sea shell to the ear produces a definite, reproducible sound. Where does this sound come from? It is clear that it is not connected to the sea as the saying goes. A widespread explanation is that the seashell amplifies the sound of the blood. One can perform two simple experiments in order to falsify this opinion:

- When the outside is quiet, one should hear the sound clearer, but the opposite is true.

- When one does some exercising (for example running), the blood streams faster; therefore the effect should be larger – in fact it is not [1].

The explanation of this sound phenomenon is the following: In our surroundings, there exists always a certain level of noise. The shell acts as a resonator which amplifies the sound at specific frequencies, which are given by the dimension and the shape of the shell. The question arises whether it is possible to include this interesting example in a more detailed, maybe also quantitative way, in the teaching of acoustics at school. We propose an approach where the teacher/student can perform a series of experiments accompanied by a computer assisted analysis.

PCs are nowadays usually already equipped with a powerful sound card. In addition there exist software programs which allow comfortable on-line data taking by microphones as well as a fast analysis of the input. The following results have been obtained with the shareware program Cool Edit [2]. The data can be visualized in form of the time-dependent pressure level; they can be Fourier transformed and presented as a frequency spectrum (the intensities of the sound at different frequencies are calculated at a given time) or as a sonagram (the time development of the spectral components is shown, where the respective intensities are indicated by different gray shading, see Fig. 1).

One can start the exploration of the sound of sea shells by the very simple experiment that one holds a hand (formed as a cup) close to the ear. One can hear some sound. The effect is much more pronounced when one takes a larger resonator, for example a cylindrical tube. Holding the tube very close to the ear changes the sound to lower frequencies. This can easily be understood and is also explained in every textbook on acoustics. Standing waves build up in the tube, and the frequencies of the fundamental and the higher modes (overtones) are related to the length L of the tube, and are given by

for a tube open at both ends (c is the speed of sound), and

for a tube closed at one end.

Fig. 1:Sonagram of the eigenresonances of a cylindrical tube. Two sides of the tube are open (left and right) and one side is open (middle) giving rise to higher/lower frequencies of fundamental and overtones.

We have used a tube with a length of 0.48 m which would theoretically give fundamentals of f₁ = 350 Hz (open at both ends) and f₁ = 180 Hz (closed at one end). The measured values were f₁ = 340 Hz and f₁ = 170 Hz, respectively. Also the difference can be understood: The “acoustical length” of a pipe is a bit longer than the real length giving rise to a slightly deeper tone [3].

The analogy of a sea shell with a cylindrical tube looks a bit crude. As a next approximation we used some plastic bottles and cups for our experiments. Fig. 2 gives the result with a plastic can. Again one can see the fundamental and higher partials, but some more comments are in order regarding these results.

Acoustical resonating systems are often associated with Helmholtz resonators. Helmholtz first described these resonators in 1860, and he used them for the spectral analysis of complex sounds. They are hollow metallic bodies in various shapes (spherical or cylindrical), some of them even tunable. There is a small hole at one end so that the sound from outside can enter the resonator. On the other side there is some small nipple which should be placed into the ear canal. The theoretical model of a Helmholtz resonator is that of a large oscillating air volume acting like a spring on the small air volume in the nipple (being the oscillating mass of the system). The corresponding eigenfrequency is given by [3,4]

,

Fig. 2: Sonagram of the frequency spectrum of a plastic can. The can is opened and closed successively. When it is closed, no noise can enter from the outside and the eigenresonances disappear.

where A and L are the cross section and length of the nipple, respectively, and V stands for the large air volume. Our examples, bottles or cans, should act in between these two models, namely ideal Helmholtz resonators and ideal cylindrical tubes, and the measured resonance frequencies confirm this statement.

Figure 2 exhibits also another sound detected at very low frequencies, i.e. around and below 20 Hz. Of course, this sound cannot be heard, it is infrasound. Nevertheless the question arises about the origin of this phenomenon. A direct hint to the explanation can be given by the following experiments: One holds the can with one or two hands; the can lies on the floor or on some table; one holds the can firmer and firmer. When the can is not held by hands, the effect disappears, and the firmer one holds the can, the larger the amplitude of the oscillation is. It is the trembling of the muscles which can be seen by these experiments: The microvibration of muscles have been found in 1943 by the Austrian neuropathologist Rohrbacher. The average frequency of a relaxed muscle is between 7 and 10 Hz, a maximally contracted muscle can have a frequency as high as 30 Hz [5].

Let us finally come to experiments with real sea shells. We recorded and analyzed the sound of two shells, Murex and Cassis (see Fig. 3). The fundamentals are clearly visible, and, naturally, the frequency of the larger shell is lower (400 Hz) than that of the smaller shell (640 Hz). The higher partials are not so clearly developed in Cassis as in Murex. Due to the complicated geometry of the shells, the overtones are not multiples of the fundamental. From the frequencies of Murex (640, 1350, 2090, 2870 Hz) one could be tempted to read off a similarity to the law of a tube. This mixture of overtones which are not perfect multiples of the fundamentals and the appearance of rather broad resonances give rise to the impression of a non-technical, natural sound, as from the sea; thus we finally come back to our headline.

Fig. 3: Sonagram of the sound of two shells, Murex (left) and Cassis (right).

We have tried to present an example, where one starts with a question which might be of interest to the students. Guided by the teacher, students can approach the final answer by some experiments accompanied by theoretical considerations. The computer assisted analysis should not be a barrier but an additional motivational component for the students, and for the teachers as well.

[1] G. Rosenberg, American Conchologist, March 1995, p. 21.

[2] Cool Edit 2000 by Syntrillium Software Corporation; http://www.syntrillium.com.

[3] M.P. Silverman, E.R. Worthy, The Physics Teacher 36 (1998), p. 70.

[4] T.B. Greenslade, Jr., The Physics Teacher 34 (1996), p. 228.

[5] http://www.studio32.net/WWW/Portfolio/Optimalife/TheoreticalBasis.html.