Unit 1 Exam Study Guide
Unit 1 Exam Study Guide PHYS 1270
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This 5 page Study Guide was uploaded by Kait Brown on Sunday September 18, 2016. The Study Guide belongs to PHYS 1270 at University of North Texas taught by Cheryl Lawler in Fall 2016. Since its upload, it has received 41 views. For similar materials see Science and Technology of Musical Sound in Physics at University of North Texas.
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Date Created: 09/18/16
Study Guide PHYS 1270.001 Science and T echnology of Musical Sound Unit one Sound is a mechanical (longitudinal) wave that originates from a vibration and travels through a material medium (air, water, solid). It has a frequency between 20 Hz and 20 kHz. A wave is a change or disturbance that travels from one place to another. Mechanical waves require some source of some physical mechanism through which elements of the medium canurbed, and influence each other. Remember, though sound is wave, the wave is caused by an oscillation of a body. Longitudinal waves move along the direction of propagation of the wave. Transverse waves move perpendicular to the direction of propagation of the wave. Radio waves are not sound. Instead, like light waver, they are oscillations in the electromagnetic force field (meaning they’re electromagnetic waves instead of mechanical waves) and require no medium. Sound information is coded in the amplitude (AM) or frequency (FM) of the radio waves. Lightning is a high energy electrical discharge. When lightning strikes, the air gets very hot very quickly, causing the particles to explode. This explosion sound sends a shockwave to our ears, allowing us to hear thunder. Velocity of a wave is the distance a point on the wave travels in an allotted time. The formula for this is v=d/t. Sound is nondispersive. This means that its velocity is in no way affected by its frequency. No matter how many waves are produced by a particular sound, the velocity of the waves produced by that sound will ALWAYS be the same. At room temperature of 20° the velocity of sound is always 343 m/s. All waves share certain characteristics, like the transfer of energy (waves don’t transfer matter). Most convenient approximation of the relationship of sound velocity and temperature: V=[343+.6(T-20C)] m/s. This means that for every degree above (or below) room temperature (20°C) the speed of sound increases (or decreases) by .6 m/s. The speed of sound in air depends on the temperature because disturbances in air (sound waves) are transmitted by collisions between air particles. Between collisions, the particles move freely, and (for a given density) their speed determines how quickly one collision follows the next. The air temperature, T, is a measure of speed of the air particles. Sound travels faster in warm air than cold because the air molecules are moving faster when hotter. Speed is proportional to the square root of T. v∞√T A sound wave is a pressure wave. Regions of high compressions of low pressure (rarefactions) are established as the result of the vibrations of the sound source. The compressions and rarefactions result because sound is denser than air and has more inertia. Waves have a speed that is dependent only upon properties of the medium. The warmer or colder the air, the more quickly or slowly, respectively, sound travels through it. The longitudinal movement of air in a sound wave produces pressure fluctuations. A simple harmonic oscillator is a type of periodic motion for which the restoring force is proportional to the displacement from the equilibrium position (the amount of force it takes the object to get back to its starting point is the same amount required for it to get to the end position) and the restoring force and displacement have opposite directions (up and down, left and right, etc.) Hooke’s Law is an accurate approximation for the behavior of most solid bodies, as long as the forces and deformations are small enough. However, many solid bodies are not small enough, so they may be modeled as elastic objects that obey Hooke’s Law (like a spring with a mass attached). Hoooke’s Law: F=-k•x Natural Frequency of SHO: f=1/(2π)•√(k/m) The number of normal or natural modes of vibration of an oscillator is equal to the number of simple harmonic oscillators that the complex oscillator comprises. Complex vibrational motion can be analyzed as the combination of natural modes of oscillation by SHOs that execute sinusoidal motion. A sine wave describes anything that varies with time or position, like the trigonometric function called “sine”. A simple harmonic oscillator moves like a sine wave. Its motion is called sinusoidal. Any sound that comes from an instrument is a complex sound. A complex waveform is the addition of more than one single frequency. These waveform are not readily analyzed by eye as their shape varies according to the phase relationships of the various component tones. As complex waves increase in complexity, it becomes increasingly difficult to determine anything from their waveform except for the fundamental frequency. The Fourier Analysis is the decomposition of a wave into the sine wave components from which it can be built up using a process called the Fourier Synthesis. A Fourier Analysis is a representation of all the components that a waveform comprises amplitude versus frequency, and phase versus frequency. As waves travel, they set up patterns of disturbance. The amplitude of a wave is its maximum disturbance from its undisturbed position. A line spectrum displays the frequencies and relative amplitudes of the component sine waves. Each sine wave is displays as a single vertical line placed at the appropriate frequency on the x-axis. The height of the lien represents the amplitude of the component since wave. Amplitude is usually displayed as a relative sound pressure level (Pa) or as a decibel value. Phase information is absent in such a display since phase is inaudible to human beings. The envelop of a tone is the variation of its amplitude versus time. Musical tones have four main parts of their envelop: the attack, the decay, the sustain, and the release. The phase of a wave is how much the start of the wave is delayed or advanced in time. A harmonic series has components that are integral ratios of each other. The first harmonic is called the fundamental. Humans infer fundamental frequency in a harmonic series even if it is missing or inaudible (Ohm’s Law for Sound). An octave is a musical term for two tones that have a frequency ration of 1:2. A square wave is made up of only odd harmonics. Resonance between two oscillations requires that frequencies match well. Wavelength o Λ o Measured in meters o Distance from one point on a wave to a corresponding point (point of the same phase) on the next cycle Amplitude o A o Maximum change in any variable during each cycle of a vibratory disturbance o Maximum excursion from equilibrium o Unit for pressure wave: Pascal [Pa] o Unit for displacement wave: meter [m] Frequency o F o Measured in Hertz (Hz) o 1/sec o The number of cycles per second o f=v/λ Period o P o P=1/f o Number of seconds per cycle Velocity o V o Distance moved/time moved o v=λ/P o v=λ*f o A.K.A. Chain of Inference Pressure o P=F/S o Force per unit Area (S) o The unit of pressure in SI units is the Pascal [Pa]=1 Newton/m2 o Standard atmosphere=1.0 atm o 1 atm ≅ 105N/m2=105 Pa=102*103 Pa =100 kPA ≅ 14.7 psi
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