• Laboratory 2: Resonance, Time/Frequency Analysis

Week 2

• Homework: Waves and resonance problems

Laboratory 2: Resonance, Time/Frequency Analysis

• View traveling- and standing-wave motion on a string using the Matlab script pluckview.m

• View standing-wave motion on a string using Max Mathews' driven string system.

• (From Benade, Fundamentals of Musical Acoustics, pg. 171) When one strikes the G$_{4}$ key of a well-tuned piano, the strings vibrate with the following list of harmonically related characteristic frequencies: 392, 784, 1176, 1568, 1960, 2352, ...Hz (ignoring the slight inharmonicity of real strings). All of these components serve to drive the soundboard, and thence everything else that it is connected to, including the strings. If we slowly but fully depress the key for G$_{3}$ in order to raise the damper for that note without striking the strings, we supply ourselves with a system whose natural frequencies are as follows: 196, 392, 588, 784, 980, 1176, ...Hz. Striking the G$_{4}$ key (while the G$_{3}$ key is still being silently depressed) and releasing it quickly will provide a short burst of excitation to the even-numbered modes of the G$_{3}$ strings, and these will continue to sing after the direct sound of the G$_{4}$ strings has been killed off by their damper touching them on the release of the key. Why do we hear a pitch belonging to G$_{4}$ coming from the open G$_{3}$ string in this experiment? Reversing the experiment, so that the G$_{4}$ key is held down and the G$_{3}$ key is struck briefly, produces a closely similar result, with a similar explanation. Your understanding of what is going on here will be improved if you observe what happens when G$_{3}$ is replaced by F$_{3}\sharp$ or G$_{3}\sharp$, with the G$_{4}$ key being used as before.

• Record a few hard striking sounds (impulsive sounds) and a few ``steady-state'' sounds (whistling or singing a steady tone), being careful not to ``clip'' the signals during the recording process. View the time-domain waveforms and their associated time-varying spectra using snd. What general observation can be made regarding the frequency content of these two types of sounds? Also, consider aspects of partial ratios, partial strengths, and partial decay rates.