Photo Gallery of PHYS-482, Acoustics II: Sound & Vibration

The greater part of this advanced elective course is lecture based - we discuss vibration of simple and complex systems, circuit analogies for mechanical and acoustical systems, loudspeaker design and performance, coupled oscillating systems, the vibrating string, acousic waves in solids (longitudinal, torsional and bending), experimental modal analysis, sound transmission through walls, and other sound-structure topics. However, while we do spend most of our time in the classroom, this course is usually small enough (6-8 students) that after every 4-5 lectures or so we take a "field trip" to the acoustics lab and get some hands-on experience playing with the systems we've been discussing in the classroom. These field trips are not full-blown laboratory experiments, but are intended to provide students with the opportunity to see the theory in action, and to learn some of the ways in which theory is only able to approximately describe real systems. A full blown laboratory course (PHYS-484, Acoustical Measurements) is available for students who wish to gain more laboratory experience with acoustical equipment and phenomena.

Damping Mechanisms

A pop bottle with a small amount of cotton inserted into the neck acts as a very nice example of a damped acoustic oscillator (otherwise called a Helmholtz resonator). The volume of air in the cavity provides the springiness while the "plug" of air in the neck provides an inertia (mass) effect as it oscillates in and out of the neck opening. A microphone is inserted into the acoustic cavity of the pop bottle to measure the variation in pressure - analogous to measuring the motion of a mass-spring system, and the bottle is acoustically excited by sound waves from a loudspeaker. Sweeping through a range of frequencies and recording the resulting microhone response with a Frequency Analyzer the students are able to obtain a frequency response curve with a peak indicating the resonance frequency. The height and broadness of the peak indicate the amount of damping. By changing the amount of cotton in the neck, students are able to see the effect of various damping amounts on the resulting frequency response curve. By recording the frequency and amplitude of the peak, as well as the frequencies at which the amplitude is 3dB less than the peak, students are able to estimate the damping coefficient for this damped system.

In a second damping experiment students extract the damping constant of a system by observing the amplitude as it decays with time. We use a pendulum which consists of a large board suspended from strings. Upon being released the pendulum swings back and forth, but loses energy to aerodynamic drag forces so that the amplitude decreases with each oscillation. Plotting the amplitude as a function of time results in a roughly exponential decay curve^* and students can estimage the damping constant using the logarithmic decrement.

^*Exponential decay is the result of a viscous damping force which is proportional to velocity. Aerodynamic drag forces are actually proportional to velocity. However, with an appropriate conversion factor it is still possible to extract the actual damping rate from the exponential decay curve.

Vibration of a Multiple-Degree-of-Freedom System

Whiffle golf balls and rubber bands make for an easy to assemble demonstration of a vibrating system with a finite number of degrees of freedom. Each whiffle ball provides local mass, while the rubber bands provide the elastic restoring forces. A single ball system has one resonance frequency. A two-ball system has two resonances, one in which both balls move in the same direction and a second mode in which both balls move in opposite directions. A three-ball system will have three resonant modes, etc. In this hands-on session students try to guess the mode shapes and relative frequencies as they continue adding balls to the system.

Animations of a Mulit-dof system

The Vibrating Fixed-Fixed String

An elastic string, fixed at both ends, is a very common experiment that almost all physics students encounter at some point in a lab. The students shown below are using a strobe light and the phenomenon of aliasing to "freeze" the vibration in time and watch the string appear to vibrate in slow motion. They are also looking at the effect on the vibrational amplitude of the string as a function of driver location. And finally, they are looking at the effect on the mode shapes and frequencies when a point mass is attached to the mid-point of the string.

Longitudinal Waves in an Aluminum Rod

In the photos below students are observing longitudinal waves in an aluminum rod. One student (Brian Basset, AP/ME '05) is tapping one end of the rod with a force hammer to exite it into vibration while the other student (Nick Clute, EE /05) is using a frequency analyzer to look at the response of an accelerometer attached to the other end of the rod. The time delay between the hammer impulse and the accelerometer response signal can be used to calculate the speed of sound in aluminum. The frequency spectrum can be used to verify that longitudinal waves obey a harmonic series (higher frequencies are integer multiples of the lowest frequency standing wave, called the fundamental), and also to measure the speed of sound. Comparing results for a steel rod with the same dimensions allows for comparison of the sound quality, frequencies, and sound speed.

Chladni Patterns in Vibrating Plates

Two-dimensional standing waves in a vibrating plate may be observed by driving the plate at one of its resonance frequencies and sprinkling sand on the plate. As the plate vibrates the sand collects along the nodal lines (points on the plate that do not move while the plate is vibrating) forming Chladni patterns - named after the German physicist who discovered them back at the end of the 18th century. The students in the photos are trying to find as many different Chladni patterns as they can for circular and square plates, attempting to decipher the mode number designation for each pattern.

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