Question

The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck

Other
ANSWERED
asked 2021-02-26
The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then?

Answers (1)

2021-02-28
As the string is vibrating in its fundamental frequency
\(\displaystyle{L}=\frac{\lambda}{{2}}\)
\(\displaystyle\lambda={2}{L}={2}\cdot{0.64}{m}={1.28}{m}\)
The speed of the wave in the string is
\(\displaystyle{V}={f}\lambda={330}\cdot{1.28}={422}{H}{z}\)
a) If the string is stopped by a fret then
L = (2/3)0.64
so \(\displaystyle{\left(\frac{{2}}{{3}}\right)}{0.64}=\frac{\lambda}{{2}}\)
\(\displaystyle\lambda={0.853}{m}\)
frequency \(\displaystyle{f}_{{{1}}}=\frac{{V}}{\lambda}\)
= 422Hz / 0.853 = 495 Hz
b) When plucking the string at one sixth the way of the lengthof the string
\(\displaystyle{2}{L}={3}\lambda\) ( the string vibrates with third resonance Possibility)
\(\displaystyle\lambda={0.4266}{m}\)
frequency \(\displaystyle{f}_{{{2}}}=\frac{{422}}{{0.27}}{m}={990}{H}{z}\).
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-06-10
Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.
asked 2021-03-24
A 2.4-kg object is attached to a horizontal spring of forceconstant k=4.5 kN/m. The spring is stretched 10 cm fromequilibrium and released. Find (a) the frequency of themotion, (b) the period, (c) the amplitude, (d) the maximum speed,and (e) the maximum acceleration. (f) When does the objectfirst reach its equilibrium position? What is itsacceleration at this time?
Two identical blocks placed one on top of the other rest on africtionless horizontal air track. The lower block isattached to a spring of spring constant k= 600 N/m. Whendisplaced slightly from its equilibrium position, the systemoscillates with a frequency of 1.8 Hz. When the amplitude ofoscillation exceeds 5 cm, the upper block starts to slide relativeto the lower one. (a) What are the masses of the twoblocks? (b) What is the coefficient of static frictionbetween the two blocks?
asked 2021-02-25
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
asked 2021-05-09
A pair of speakers separated by .700 m are driven by the sameoscillator at a frequency of 690 Hz. An observer originallypositioned at one of the speakers begins to walk along a lineperpendicular to the line joining the speakers.
a. How far must the observer walk before reaching a relativemaximum in intensity?
b. How far will the observer be from the speaker when the firstrelative minimum is detected in the intensity?
asked 2021-05-20
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let \(\displaystyle{F}_{{R}}\) be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
asked 2021-02-17
Two pieces of steel wire with identical cross sections have lengthsof L and 2L. Each ofthe wires is fixed at both ends and stretched so that the tensionin the longer wire is five timesgreater than that in the shorter wire. If the fundamental frequencyin the shorter wire is 60 Hz, what isthe frequency of the second harmonic in the longer wire?
asked 2021-04-13
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.
asked 2021-05-12
4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
asked 2021-03-26
A helicopter carrying dr. evil takes off with a constant upward acceleration of \(\displaystyle{5.0}\ \frac{{m}}{{s}^{{2}}}\). Secret agent austin powers jumps on just as the helicopter lifts off the ground. Afterthe two men struggle for 10.0 s, powers shuts off the engineand steps out of the helicopter. Assume that the helicopter is infree fall after its engine is shut off and ignore effects of airresistance.
a) What is the max height above ground reached by the helicopter?
b) Powers deploys a jet pack strapped on his back 7.0s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s2. how far is powers above the ground when the helicopter crashes into the ground.
asked 2021-03-11
In one of the original Doppler experiments, a tuba was playedon a moving flat train car at a frequency of 75 Hz., and a secondidentical tuba played the same tone while at rest in the railwaystation. What beat frequency was heard if the train car approachedthe station at a speed of 10.0 m/s?

You might be interested in

...