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 W/ACCESS
Additional Engineering Textbook Solutions
Vector Mechanics For Engineers
Mechanics of Materials (10th Edition)
Database Concepts (8th Edition)
Electric Circuits. (11th Edition)
Thermodynamics: An Engineering Approach
Modern Database Management
- A 100 m length of a smooth horizontal pipe is attached to a large reservoir. A attached to the end of the pipe to pump water into the reservoir at a volume flow rate of 0.01 m³/s. What pressure (gage) must the pump produce at the pipe to generate this flow rate? The inside diameter of the smooth pipe is 150mm. Dynamic Viscosity of water is 1*103 Kg/(m.s). K at the exit of the pipe is 1. pump 10 m D=150mm L= 100 m- Pumparrow_forward: +0 العنوان solle не A 4 A numn drawe water through 200 ۳/۱ ۲/۱ A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels as shown in figure. The door is 1.2 m high and 1 m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydrostatic force on the door if it is located at the center of the door, and discuss if the driver can open the door, if not; suggest a way for him to open it. Assume a strong person can lift 100 kg, the passenger cabin is well-sealed so that no water leaks inside. The door can be approximated as a vertical rectangular plate. 8 m E ✓ Lakearrow_forwardTwo concentric plain helical springs of the same length are wound out of the samewire circular in cross section and supports a compressive load P. The inner springmean diameter 200 mm. Calculate the maximum stress induced in the spring if theconsists of 20 turns of mean dimeter 160 mm and the outer spring has 18 turns ofdiameter of wire is equal to 10 mm and Pis equal to 1000 N. (Take Ks=1)arrow_forward
- t 1+2\xi pu +962гz P 1 A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels as shown in figure. The door is 1.2 m high and I m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydrostatic force on the door if it is located at the center of the door, and discuss if the driver can open the door, if not; suggest a way for him to open it. Assume a strong person can lift 100 kg, the passenger cabin is well-sealed so that no water leaks inside. The door can be approximated as a vertical rectangular plate. 加 8 m 1.2 m Lake -20125 DI 750 x2.01 5 P 165 Xarrow_forward11. If Sin(x+α) = 2Cos(x-a); prove that: tan x= 2- tana 1-2 tanaarrow_forward12. If Sin(x-a)= Cos(x+α); prove that: tan x=1.arrow_forward
- : +0 العنوان solle не A 4 A numn drawe water through 200 ۳/۱ ۲/۱ A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels as shown in figure. The door is 1.2 m high and 1 m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydrostatic force on the door if it is located at the center of the door, and discuss if the driver can open the door, if not; suggest a way for him to open it. Assume a strong person can lift 100 kg, the passenger cabin is well-sealed so that no water leaks inside. The door can be approximated as a vertical rectangular plate. 8 m E ✓ Lakearrow_forward۲/۱ - | العنوان A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels as shown in figure. The door 1.2 m high and 1 m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydrostatic force on the door if it is located at the center of the door, and discuss if the driver can open the door, if not; suggest a way for him to open it. Assume a strong person can lift 100 kg, the passenger cabin is well-sealed so that no water leaks inside. The door can be approximated as a vertical rectangular plate. 8 m Lakearrow_forward- | A pump draws water through a 300-mm diameter cast iron pipe, 15m long from a reservoir in which the water surface is 4.5 m higher than the pump and discharges through a 250- mm diameter cast iron, 75 m long, to an elevated tank in which the water surface is 60 m higher than the pump. Q-0.25 m³/s. Considering f- 0.02 and the coefficients for minor head losses (k entrance 0.5, k bend 0.35, and K exit -0.5), compute the power of the pump. Kexit 250 mm dia 75 m Length 60 m العنوان 300 mm dia. 15 m Length -UZ kentrance 11421 Kpend osthor oster ۲/۱arrow_forward
- A heavy car plunges into a lake during an accident and lands at the bottom of the lake on its wheels as shown in figure. The door is 1.2 m high and 1 m wide, and the top edge of the door is 8 m below the free surface of the water. Determine the hydrostatic force on the door if it is located at the center of the door, and discuss if the driver can open the door, if not; suggest a way for him to open it. Assume a strong person can lift 100 kg, the passenger cabin is well-sealed so that no water leaks inside. The door can be approximated as a vertical rectangular plate. 8 m m Lakearrow_forward۲/۱ A pump draws water through a 300-mm diameter cast iron pipe, 15m long from a reservoir in which the water surface is 4.5 m higher than the pump and discharges through a 250- mm diameter cast iron, 75 m long, to an elevated tank in which the water surface is 60 m higher than the pump. Q = 0.25 m³/s. Considering f= 0.02 and the coefficients for minor head losses (k entrance = 0.5, k hend 0.35, and K exit -0.5), compute the power of the pump. 4.5 m 300 mm dia. 15 m Length 250 mm dia. 75 m Length kentrance kexit 60 m kbend ostherarrow_forwardA pump draws water through a 300-mm diameter cast iron pipe, 15m long from a reservoir in which the water surface is 4.5 m higher than the pump and discharges through a 250- mm diameter cast iron, 75 m long, to an elevated tank in which the water surface is 60 m higher than the pump. Q = 0.25 m³/s. Considering f= 0.02 and the coefficients for minor head losses (k entrance = 0.5, k hend = 0.35, and K exit 0.5), compute the power of the pump. = 4.5 m 300 mm dia. 15 m Length 250 mm dia. 75 m Length Kentrance kexit 60 m kbendarrow_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