Acoustic vibration … in a kazoo?

Kevin J. Farrell, Principal Engineer, Computational Simulation & Validation

While visiting my favorite used bookstore, I spotted a display of kazoos near the cash register. I was going to teach HTRI's Vibration Analysis Short Course in a few days and thought I could reinforce some important concepts in the course by explaining how kazoos work. Plus, I remembered having fun playing a kazoo when I was (much) younger.

So I bought one (Figure 1) for the grand price of US$3.99.

What is a kazoo and how does it work?

Kazoos, along with drums and tambourines, belong to a class of instruments called membranophones. These instruments have stretched skins or membranes that vibrate when excited, either by breath or touch. Membranophones are some of the oldest instruments in existence. Modern metal kazoos, like the one I purchased at the bookstore, are usually attributed to G. D. Smith's invention in the early twentieth century [1].

Figure 2 highlights the principal features of a kazoo. When you blow into the mouthpiece of a kazoo, the internal membrane vibrates sympathetically and produces the same pitch as the input hum but with a richer tone quality that musicians call timbre.

What's so interesting about a kazoo and its vibration?

The analysis of any vibrating system—flow-induced or not—has three principle concerns.

• Excitation: Type, location, amplitude, frequency
• System: Mass, stiffness, damping
• Response: Type, location, amplitude, frequency

The kazoo and the shell-and-tube heat exchanger experiencing acoustic vibration manifest the same response—namely radiated noise—via sympathetic resonance.

In the kazoo, the excitation is provided by the human vocal cords (the hum), and the system is the membrane in the trumpet of the kazoo. The internal void of the kazoo between the mouthpiece and the escape hole is a fluid path for the hum to reach the membrane. For the kazoo, amplification via resonance is assured because the kazoo is tuned to frequencies in the range of the human voice (about 90 to 255 Hz).

In a shell-and-tube heat exchanger, the unsteady pressures in the wakes of the cross flow may lock on to the natural frequencies of the gas volume in the shell (the system). Fortunately, in the shell-and-tube exchanger, engineers can “detune” the system to mitigate the occurrence of resonance.

So how would an engineer (me) test the vibration of a kazoo?

First, I used a cell phone to measure the time history of sound from my hum with and without the kazoo. I described how to do this in a previous newsletter article [4]. Figure 3 shows the frequency content of the humming after I applied the Fourier transform of the sound records (*.wav files).

Clearly, the sound is amplified for the first three membrane modes, notwithstanding my ability to maintain pitch and sound volume during the test. Now we have a working definition of timbre for us non-musicians.

While engineers work diligently to mitigate the acoustic vibration potential in shell-and-tube heat exchangers, we can still appreciate the simple kazoo because of its acoustic vibration. However, our hope is that we can't hear it anywhere else in the plant!

References

1. G. D. Smith, Musical Toy, U.S. Patent No. 700,986 (1902).
2. B. Stewart, The Complete How To Kazoo User's Guide & Practioner's Manual, Workman, New York (2006).
3. B. S. Rajaratnam, D. S. Kumar, A. B. R. Lidiya, K. Y. Chang, H. M. G. Loh, J. Y. L. Lim, J. Wee, and L. Zhang, A pilot study to evaluate if the introduction of a kazoo (a portable musical instrument) to improve lung function of adults with cerebral palsy, Medical and Dental Research 1(2), 1 — 3 (2018). doi: 10.15761/MDR.1000109
4. K. J. Farrell, Measuring sound... with a phone?, https://www.htri.net/news/measuring-sound---with-a-phone (15 Dec. 2024).