The wind chimes enjoyed by western cultures today are typically made from rods of varying lengths  suspended from a rack. This design became popular in the 19th century.  This design is partly due to a musician who sought to improve the tone of the bells he played in an orchestra. Entrepreneurial Victorians, remembering the Japanese furin, popularized this design.

Author’s Wind Chime

The wind chime model is “Cavernous Echoes” by Majesty Bells, as shown in the image at the top of the page. The  vendor’s  brochure  states that this is a five note wind chime hand-tuned to the scale of  E. The material  is anodized aluminum.   The outer diameter is 1.25  inch. The chimes are hollow, with  a wall  thickness of 3/32  inch.   The boundary condition is essentially free-free for vibration calculations.  The condition is open-open for acoustic frequency.

The chimes have three wooden parts, which are from top to bottom: the head, the striker, and the wind catcher.

Experiment

Assume that the wind chimes have three types of possible responses as shown  in Table 1. Furthermore, each type has higher modes.  One of the objectives is to determine which mode type or types produce  the  chimes pleasing sound.   The natural frequencies are calculated using textbook formulas.

In  addition, the chimes also have a ring frequency corresponding to a breathing mode.  This frequency is 50,540 Hz for each chime, since the chimes have a common diameter. This frequency is well above the upper frequency limit of human hearing, however.

The wind chimes were excited  separately using the striker. The resulting responses were due to the  bending modes in each case. Note that the bending mode is the only type in Table 1 that has non-integer harmonics, however.  In this sense, wind chimes are atonal.

Frequency Response Data

The response data is summarized in Table 2. The musical note is the nearest note to the measured frequency.

The sequence: E, F#, G#, A, B, represents the first five tones of the E major scale.  The complete E major scale contains this sequence plus C# and D#.

The second natural frequency of each chime represents a note in the E scale, as shown in Table 2.

Table 1. Wind Chime Fundamental Frequencies

Table 2. Measured Frequencies and Nearest Musical Notes

Sound Files

Waterfall Plots

Waterfall plots for each of the five chimes are given in Figures 1 through 5, respectively. The vertical  axis is the Fourier transform magnitude, which has an arbitrary scale factor.  Each axis scale is linear.

The corresponding  frequencies for each chime are given in the accompanying tables. The calculated   frequency is the  bending frequency.  The measured frequencies have reasonably good agreement for the calculated frequency for each chime.

The waterfall plots show the relative difference in amplitude between the various natural frequencies within each chime.

The  extent to which each mode is excited depends in part on the impact location of the striker against the chime.

Whether the manufacturer considered the complexity of nodal lines when designing the striker position is unclear. The waterfall plots also show the how the reverberation time varies between the natural frequencies. The fundamental frequency is the frequency with the longest reverberation time for each chime.

The peak amplitude response, however, may occur at the second or third natural frequency for a given chime.

Bending Mode Shapes

A geometry model of chime 1 is shown  in Figure 6.

The first through third bending mode shapes are shown  in Figures 7 through 9, respectively. The  mode  shapes  are  greatly exaggerated, with an arbitrary scale factor.

Figure 6. Chime 1, Undeformed Model	Figure 7. Chime 1, First Bending Mode
Figure 8. Chime 1, Second Bending Mode	Figure 9. Chime 1, Third Bending Mode