Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation . If a tuning fork for the note above middle on an even-tempered scale has a frequency of approximately hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is millimeter, determine the equation that describes the movement of the tuning fork.
Source: David Lapp. Physics of Music and Musical Instruments. Medford, MA: Tufts University, 2003
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus & Its Applications (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
- Harmonic Motion The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=12cos6t where y is the displacement in feet and t is the time in seconds. Find the displacement when (a) t = 0, (b) t=14, and (c) t=12.arrow_forwardRefraction When you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is 1.333. This is the ratio of the sine of 1 and the sine of 2 (see figure). (a) While standing in water that is 2 feet deep, you look at a rock at angle 1=60 (measured from a line perpendicular to the surface of the water). Find 2. (b) Find the distances x and y. (c) Find the distance d between where the rock is and where it appears to be. (d) What happens to d as you move closer to the rock? Explain.arrow_forwardFrequency With simple harmonic motion, the reciprocal of the period is called the frequency. The frequency, given by f=1/period represents the number of cycles (or oscillations) that are completed per unit time. The units used to describe frequency are Hertz, where 1HZ=1 cycle per second. Alternating Current In Europe, the voltage of the alternating current coming through an electrical outlet can be modeled by the function V=230sin(100t), where t is measured in seconds and V in volts. What is the frequency of the voltage?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning