SIGNALS & SYSTEMS IN MUSIC CREATED BY P. MEASE 2010 Resonant Self-Destruction OBJECTIVES In this lab, you will measure the natural resonant frequency and harmonics of a physical object then use this information to destroy it. INTRODUCTION & BACKGROUND Resonance: We obtain this synthesizer effect by boosting the frequencies right around the cutoff of the filter. This may seem a little odd in the scope of electronics at first so how about a formal definition (and I quote Merriam- Webster): 1 a : the quality or state of being resonant b (1) : a vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system (2) : the state of adjustment that produces resonance in a mechanical or electrical system 2 a : the intensification and enriching of a musical tone by supplementary vibration [1] Natural resonance is possessed by all physical objects since anything can vibrate. Resonance is the frequency at which this mass will choose to oscillate the most. Resonance can be a good or bad. Musical instruments are designed to take advantage of resonance to increase volume or control its timbre. When the strings of a violin, for example, are bowed, the sound resonates within the body, which is the hollow part of the instrument, and thus becomes a bit more amplified for us to hear. If you are bridge designer, well: Tacoma Narrows collapse in 1940 caused by aeroelastic flutter, an uncontrolled oscillation. P.Mease 2010 Signals & Systems in Music Resonant Self-Destruction 1
Just like physical bodies can have a natural resonance, so can electronic circuits. Some circuits, just like the bridge example, will oscillate uncontrollably. Good-ol-fashioned feedback is a form of this. Filters can be designed to be resonant as well. A LPF with resonance about the cutoff will have a frequency response that looks like: Note the boost right around the cutoff frequency of the filter. EQUIPMENT & SOFTWARE Headphones/Speakers Function Generator Laptop/PC Cabling Provided wine glass Horn Driver & Amplifier (common) PULSE Spectrum Analyzer Station (common) Earplugs Safety Glasses PROCEDURE More on resonance: Resonance can be a distinct part what makes an instrument sound like a particular instrument. The resonance in your voice makes it different from the one that s next to you. There are tones you can produce with your voice that resonate in different areas of your body. There is a common part of our speech that resonates predominantly in the chest area, or rather, the voice that we are used to, talking. There is also the head voice, which the sound resonates primarily in the head. A lot of pop singers use a mix which let the sound resonates in their nasal passages. This is not singing out of your nose, but producing a natural tone with a personal presence. The nasal passage (cavity) is like an acoustic cabinet which renders some of the most distinct features of one s voice. Now let s try some experiments. P.Mease 2010 Signals & Systems in Music Resonant Self-Destruction 2
Human vocal cord (and yes, that is what s in your throat) anatomy. [2] - Pre-experiment: Place one hand on your upper chest just below the neck and the other on the side of your head (your cheek). Now sing a high note (preferably one that you can sustain) and then slowly move to the lower part of your voice register. A smooth transition from the top to bottom notes creates what is known as portamento and will sound like you re yawning after a long nap. Go as low as you can. - While you re doing this, you will find pitches where your voice vibrates very much in the head and others where your chest vibrates more. Generally, the higher you go, the more the head voice register of your body resonate from your chest all the way to your head. You are feeling the natural resonances of two of your tone-making chambers. This resonant frequency (where your chamber vibrates excessively ) is controlled by many parameters, such as volume, length, your vocal chords, phlegm, etc - A key thing to note here is that you can clearly recognize the distinction between resonances of the different parts of your body. PAUSE, take a breath We will now identify and utilize resonance to shatter a perfectly good and unsuspecting wine glass. NOTE: YOU MUST WEAR SAFETY GLASSES FOR THE ENTIRETY OF THIS SECTION. - At your station, tap your wine glass with your finger and listen to the tone produced. Now output a sinusoid from the function generator to the PC speakers and try to tune to the wine glass fundamental frequency. AT THE PULSE STATION: Here you will measure the resonant frequency of your glass using a high accuracy audio spectrum analyzer. P.Mease 2010 Signals & Systems in Music Resonant Self-Destruction 3
- Carefully hold the microphone near the wine glass (and pointing at it). With the provided mallet (with the plastic-tipped end), tap the wine glass and observe the spectrum. You are trying to locate the glass natural resonant frequency (and its harmonics). You may have to tap it a few times to get a good strike. Be certain not to strike the glass too hard! When you find the highest peak, zoom in and place the tracer right at the point of the spike. As accurately as you can, record where the peak is located. Also record the frequency value of the 2 nd harmonic (a.k.a. first harmonic overtone). AT THE DRIVER STATION: Here you will vibrate your glass at its resonance frequency. - At the driver station, place your wine glass in the specified location. - We are using a horn driver to vibrate the glass. This is similar to a speaker, but is refined to operate at higher frequencies. The drivers we are using cannot reproduce sound below 800Hz and are more efficient the higher you go. In addition, these drivers can be very easily damaged by low frequency/dc levels. To ensure that we are not allowing these frequencies to pass, we will use an active crossover. This device is essentially a filter that only lets certain frequencies pass. For the horn driver we will use the high-pass filter set with a cutoff around 800Hz. - Turn on the function generator and set the amplitude to 100mV and turn the amplifier gain all the way down. Set the function generator frequency to the resonant frequency you recorded. If your glass fundamental resonant frequency is less than 850Hz, set it to the frequency of the 2 nd harmonic instead. Make sure the function generator is set to the sinusoid wave. -! IMPORTANT! DO NOT DO ANYTHING UNLESS THE INSTRUCTOR IS PRESENT! - Read the above bullet again ^. IF AND ONLY IF the instructor is present, install your (and all other students in class (instructor will notify!) earplugs. Make sure yours and all other students in the class safety glasses are on! - Ensuring all bodies are clear at least 5 radius from the glass, set the function generator to output a sinusoid at 800mV pp. DO NOT EXCEED 800mV pp! Increase the gain of the power amplifier until the wine glass shatters OR you hit 28dB (20dB if using the small driver). DO NOT EXCEED a gain of 28dB (20dB if using the small driver). Listen to the tone you may notice that when you ve locked on the resonant frequency of the glass the volume will slightly increase. NOTE: If the wine glass does not break, the resonant frequency you selected may be a bit off (or the glass is particularly strong). Vary the function generator s frequency by increments of 0.1Hz up and down from the peak you initially found. You can insert a plastic straw inside the glass, you can see how close you are by how much the straw dances inside the glass. If it is not dancing, you are not causing the glass to resonate. - Do not touch the broken glass; leave it at the station. DELIVERABLES Be sure to submit the following (work as a group) in your lab report. Be concise in your statements. Quality is extremely important, not quantity! Name some parameters of an object that may control the resonate frequency. Ear tuned glass frequency. Actual resonant frequency of your wine glass (both the fundamental and the 2 nd harmonic). If your glass didn t break at exactly this frequency, list the actual frequency used as well. P.Mease 2010 Signals & Systems in Music Resonant Self-Destruction 4
Why can we still break the wine glass when driving it at one of the overtone harmonics instead of just at the fundamental? Do you think there is more than one vibrating mode for the glass? How do you know (proof)? Brief list of contributions by each team member and out-of-class meeting time(s). Be sure to spend ample time discussing both results and the solutions with your entire team. Be thorough and precise in your statements. If you have any questions, please ask before submitting. SAFETY & LAB PROTOCOL - Be sure to turn down any headphone volumes BEFORE putting them on your head! - If using the headphone distribution amp, be sure to notify others wearing connected headphones when you are going to play something - Do NOT adjust any other headphone volume control but your own - Return all cabling neatly to the racks - Take extreme care handling the instruments - Clean your workspace when finished your experiment - No food or drink allowed in the lab - Wear earplugs when dealing with high SPLs - Heed all warnings throughout the lab REFERENCES [1] "resonance." Merriam-Webster Online Dictionary. 2008. Merriam-Webster Online. 7 May 2008 http://www.merriam-webster.com/dictionary/resonance [2] Image Source: http://notsosynonymous.tripod.com/images/cords.jpg P.Mease 2010 Signals & Systems in Music Resonant Self-Destruction 5