The Physics of Music
Carolyn Renee DardenAcademic Setting
I have been teaching for two years at Truman Middle School. Truman is located on the West Side of town. The population of this school is roughly 80.4% Hispanic, 4% Native American, 10.6% Anglo, 4% African American, .5% Asian and .4% other ethnicities. Out of the 650 students who attend Truman, 117 are living in poverty; that is nearly 20% of the student body. In addition, 12% of parents are unemployed and 9% are receiving public assistance. The free and reduced lunch program for A.P.S. is utilized by 79% of the students. It is also known that many of the parents have two jobs. Consequently, many of the children of these parents do not see them for days on end. This is a frightening prospect. Many teenagers are also taking care of younger siblings.
Academically, these students are also in need. With parents gone much of the time, there is little or no assistance or encouragement with homework. The educational background of these parents also has some bearing on how well these students perform academically. The Census Data of 1990 revealed 29% of adults 25 and older in the Truman community had not received a high school diploma. Of this 29%, 19% had 9-12th grade, and the remaining 10% had less than a ninth grade education. This is to be compared to Albuquerque in general where18% are without a diploma.
There is a very active gang life on the West Side. The administration is constantly watchful for all sorts of gang-related behavior. The dress code is one way of circumventing gangs and, with hope, the adults are able to identify gang-related behavior. Certain teens will wear a specific type of shirt to display their identification with a gang. People and children are resourceful. There are many different ways to distinguish one group from another. There are a few of ways gangs identify themselves: shave an eyebrow, comb hair in a certain way, tattoos, or marking ones belongings with a specific color or design. I think this is significant because the violence and peer pressure that my students are exposed to affects how much they can concentrate in class. As a result, I am competing for their attention. Music is a powerful tool to capture it.
A large percentage of the student body is non-English speaking. Many of the children at Truman speak Spanish in their homes and English at school. Some are proficient at English, yet others cannot speak or read the language that is predominately used in the United States. Truman test scores are very low in comparison to nation-wide reading and mathematics averages. The average reading level of all sixth, seventh and eighth graders is third grade. The same is true for our mathematics scores. Is education not being emphasized in the home? Or is it that many of the students are simply not familiar with the English language?
My class is a seventh grade math and science block. Basically, I have these students for 45 minutes to teach them mathematics and 45 minutes to teach them science; back-to-back, we have 90 minutes. If a lesson requires, I can teach science for the entire 90 minutes. The reverse is also true. Because the reading and mathematics’ scores at Truman average at the third grade levels, the students need as many hands-on manipulatives as they can get. This is true for both math and science. It is also my philosophy that all learners need to have access to the three different types of learning styles: seeing, hearing and touching.
This curriculum unit is focusing on the physical aspects of sound, sound waves, and the exploration of this through music. This unit will be a three-week unit. Through class exploration, the students will discover how sound is made. They will discover different types of waves (i.e., transverse and longitudinal waves). Another way will be through the use of instruments and other common household objects. Science is a process of being a discoverer. One has to observe, question, hypothesize and conclude about one’s experience. In life this is critical to becoming a fully functioning human. Adults are constantly making experiments to live better lives. What kind of pasta is better, faster or cheaper? What type of car should I buy given the amount of money I have to spend? Value judgements and day to day decisions are based on scientific process. This is an invaluable goal to teach children
Context and Background
Art and the study of physics are inventions that are solely human. Music, however, is a common medium for many living creatures. Birds and whales communicate with song. Lions, chimpanzees and other animals are soothed by tranquil melodies. Musical artifacts from Upper Paleolithic ritual sites have been found which are evidence of early musical ability in humans. Leonard Shlain has documented that as early as 35,000 years ago, musical instruments existed. Mankind is soothed by music. Music and physics entwined for the first time in the sixth century B.C.. Pythagoras of Samos is credited with first discovering pitch intervals (Sethares). Pythagoras discovered he could produce half the notes of an octave of music by dividing the string by whole numbers. Intervals in music, he demonstrated, had a mathematical, rational foundation (White 4).
A solid understanding of waves and how they behave is a necessary conceptual need for seventh graders because it is an essential part of physical science. This is required by the New Mexicos Science Scope and Sequence which is aligned with the New Mexico Standards for Excellence, the New Mexico Science Content Standards and Benchmarks, and the National Science Education Standards. Conveying these abstract concepts to this age is a daunting task. Waves and their media form a significant part of physics. Water, earthquakes, light and sound all travel in waves. Waves are the vibration of material or electric and magnetic fields as in light. There are two different types of waves that are discussed in physics: longitudinal and transverse. This unit will explore sound waves and their importance to music. The most interesting sound for most seventh grade children (and adults) is music. I intend to connect these two with activities and hand-on experiments. What are waves? How are they created? What kind of waves make sound? What kind makes musical sounds?
Simple Harmonic Motion
The pendulum is a type of wave pattern. If you hang a fishing weight from the end of a piece of string, you have a pendulum. They can be found in grandfather clocks and cuckoo clocks. The to and fro motion of a pendulum is regular, but not very useful for all timepieces. For example it will not keep accurate time on your wrist (and they are much too large). Galileo discovered that the time a pendulum takes to swing to and fro through small distances depends on the length of the pendulum. There is an equation for the period of a pendulum. It is T = 2??l/g, where T is the period, l is the length of the pendulum, and g is the acceleration of gravity. The back and forth motion of the swing is called the period. The pendulum’s period depends on the acceleration of gravity and length. It does not depend on the mass of the pendulum or on the size of the arc through which it swings.
Drop two balls of different mass and they accelerate at g. Let them slide without friction down the same incline and they slide together at the same fraction of g. Tie them to string of the same length so they are pendulums, and they swing to and fro in unison. In all cases the motions are independent of mass. (Hewitt 325)
The back and forth motion, also called oscillatory motion of a swinging pendulum in a small arc, is called simple harmonic motion. If you place a funnel that leaks sand at the bottom of a pendulum, the sand will make a straight line. When you do the same with a moving onveyor belt, and the belt is moving at a constant speed, it will produce a sine curve. A sine curve is a visual representation of a wave.
A sine curve
In the ocean, a wave has high points called crests and low points called troughs. The middle is the starting point from which one measures the height or the depth of the wave. This distance is called the amplitude.
The wavelength is the length of the wave. A wavelength is the length of the distance from one trough to the next trough, or crest to crest. It is the distance between any successive identical parts of the wave.
Wavelengths are measured using a variety of units of measurement. Beach waves are measured in meters. Ripples in a pond are measured in centimeters, and light is measured in billionths of a meter (nanometers).
Frequency
Lothar Cremer explains the physics of the violin:
"Frequency is inversely proportional to the length of the string; control of pitch by the positioning of the finger of the left hand is based on this principle."
The number of complete cycles per second is the frequency of a vibrating body. Paul Hewitt explains:
"the frequency of a vibrating pendulum, or object on a spring, specifies the number of to-and-fro vibrations it makes in a given time (usually one second). A complete to-and-fro oscillation is one vibration."
If one oscillation occurs in one second, the frequency is one vibration per second. If two vibrations occur in one second, the frequency is two vibrations per second, and so on. A hertz (Hz) is the measure of a unit of frequency. It was named after Heinrich Hertz, who demonstrated radio waves in 1886. One vibration per second is one hertz, two vibrations is two hertz, etc... AM radio is in kilohertz (kHz, thousands of hertz). FM radio is in megahertz (MHz, millions of hertz). Radar and microwave ovens operate at gigahertz frequencies. A radio station set at 1200 on the AM dial broadcasts radio waves that have a frequency of 1,200,000 Hz. A station set at 102.5 on the FM dial broadcasts radio waves at a frequency of 102,500,000 Hz.
If an object’s frequency is known, one can calculate its period and vice versa. A pendulum that makes two vibrations in one second has a frequency of 2 Hz. The time needed then for one vibration is ½ second. If the vibration frequency is 4 Hz, then the period is ¼ second. The period and the frequency are the inverse of each other.
Sound Transmission
The vibration of matter causes sound. Sound requires matter in order to be propagated. Sound can be conducted through matter: solids, liquids and gases. It cannot occur in a vacuum like light can. The sound that is transmitted by air or any other gas can be demonstrated by suspending a bell in a jar. As the air is removed from the jar, the ringing of the bell becomes fainter and fainter. When a vacuum is obtained, no sound can be heard. Once the vacuum is broken again the ringing becomes audible again:
The vibrating bell strikes air molecules, knocking them away from the metal surface. These molecules strike the adjacent air molecules, and they in turn strike others. Upon reaching the side of the jar, the glass walls are periodically bombarded by the molecules and set vibrating. The walls in turn set the outside air vibrating. Arriving at the observer’s ear, the disturbance strikes the eardrum, setting it into motion." (McLaughlin)
Another example of this is a tuning fork and how the sound transmits from one fork to the other.
(Hewitt 330)