A standard guitar, whether acoustic or electric, has six strings, all with essentially the same total length between the bridge and the nut at the tuning head. Each string vibrates at a different frequency determined by the tension on the string and the mass per unit length of the string. In order to create pitches (notes) other than these six, the guitarist presses the strings down against the fretboard, thus shortening the length of the strings and changing their frequencies. In other words, the vibrating frequency of a string depends on tension, length, and mass per unit length of the string. The equation for the fundamental frequency of a vibrating string is given by
Where
f = frequency [IIz]
T = string tension [N]
µ = mass per unit length [kg/m]
L= string length [ m]
Many electric guitars have a device often called a "whammy" bar or a "tremolo" bar that allows the guitarist to change the tension on the strings quickly and easily, thus changing the frequency of the strings. (Think of Jimi Hendrix simulating "the rockets' red glare, the bombs bursting in air" in his rendition of The Star Spangled Banner-a true tour de force. ) In designing a new whammy bar, we test our design by collecting data using a single string on the guitar and creating a graph of the observed frequency at different string tensions as shown.
- a. What are the units of the coefficient (16.14 )?
- b. If the observed frequency is 150 hertz, what is the string tension in newtons?
- c. If mass per unit length is 2.3 grams per meter, what is the length of the string in meters?
- d. If the length of the string is 0.67 meters, what is the mass per unit length in kilograms per meter?
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Additional Engineering Textbook Solutions
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Mechanics of Materials, 7th Edition
Engineering Mechanics: Dynamics (14th Edition)
Introduction To Finite Element Analysis And Design
Vector Mechanics for Engineers: Dynamics
DESIGN OF MACHINERY
- Vibrations Engineering: A rope of a pendulum has a length of 2 meters. What is the natural frequency of the system for small angles in hertz? (Express the final answer in 4 significant digits)arrow_forwardRefer to the Worksheet shown, set up to calculate the displacement of a spring. Hooke's law states that the force (F, in newtons) applied to a spring is equal to the stiffness of the spring (k, in newtons per meter) times the displacement {x, in meters): F= kx. ;Chapter 10, Problem 161CA, Refer to the Worksheet shown, set up to calculate the displacement of a spring. Hooke's law states Cell A3 contains a data validation list of springs. The stiffness (cell 83) and maximum displacement (cell C3) values are found using a VLOOKUP function linked to the table shown at the right side of the worksheet. These data are then used to determine the displacement of the spring at various mass values. A warning is issued if the displacement determined is greater than the maximum displacement for the spring. Use this information to determine the answers to the following questions. Write the expression, in Excel notation, that you would type into cell 86 to determine the displacement of the spring.…arrow_forwardThe gravitational constant g is 9.807 m/s2 at sea level, but it decreases as you go up in elevation. A useful equation for this decrease in g is g = a – bz, where z is the elevation above sea level, a = 9.807 m/s2, and b = 3.32 × 10–6 1/s2. An astronaut “weighs” 80.0 kg at sea level. [Technically this means that his/her mass is 80.0 kg.] Calculate this person’s weight in N while floating around in the International Space Station (z = 354 km). If the Space Station were to suddenly stop in its orbit, what gravitational acceleration would the astronaut feel immediately after the satellite stopped moving? In light of your answer, explain why astronauts on the Space Station feel “weightless.”arrow_forward
- A single degree-of-freedom linear elastic structure was subjected to a series of harmonic excitations, one at a time. The excitations had the same forcing magnitude but different forcing frequency. Forcing frequencies and observed peak steady-state displacements are shown in the graph below. Find the natural period and damping ratio of the structure. Displacement (mm) 60 50 40 30 20 10 0 0 1 2 . 3 4 Forcing frequency, f [Hz] 5 4. 6 7arrow_forwardA spring with an un-stretched length of 5 in expands from a length of 2 in to a length of 4 in. The work done on the spring is . in .lb. (A) k (2 in)2 (B) k [(4 in)? - (2 in)2] (C) - k [(4 in)? - (2 in)?] (D) k [(3 in)? - (1 in)*]arrow_forwardIf a spring with elastic constant k [N/m] is deformed at distance x [m], then its potential energy is:arrow_forward
- 1.4 If you measure the free vibration of a 4 degree-of-freedom system, how many frequency components are in principal included in the measured signal?arrow_forwardIn a belt-pulley system using a flat belt, if the cycle rate = 5, the diameter of the large pulley is 1000 mm, the belt length is 4000 mm, the bending frequency is 4 [1/s], what is the revolution of the small pulley?arrow_forwardYou need to run some vibrations tests and your lab has an accelerometer (2nd order system) that has a natural frequency (resonance) at 3,000 Hz and damping ratio of 0.05. The vibrations you wish to measure are in the range of 100 - 1,200 Hz. a. What are the amplitude error (in %) and phase shift (in degrees) expected at the upper end of the vibration frequency range (1,200 Hz)? b. What is the maximum frequency that you can measure to have no more than 1% error in the amplitude of the reading? c. Is this a suitable choice of accelerometer for this measurement? Why or why not?arrow_forward
- An object is doing a simple harmonic motion. When the vibration displacement was 0.2 m from the center of the path, the magnitudes of the velocity and acceleration were 0.75 m/s and 5 m/s^2, respectively. What is the maximum speed of this object? ans: 1.25m/s suppose COSINE harmonic function.arrow_forwardUse of Infinite Sequences and Series in Problem Solving of Special Theory of Relativity. A spacecraft travels fast the earth has a greater velocity (ⱱ) which approximates the speed of light. The time (to) measured in the spacecraft is different from the time (t) measured on earth. The time difference is given, to = t √1- ⱱ 2/c2 = t (1 – ⱱ 2/c2)1/2.arrow_forwardRate of heat transfer and rate of mass are the same in which they are a quantity but they differ in their sign convention and units. Select one: O True O Falsearrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY