A String Streched Tightly between Two Points.

[chikis]

A string is stretched tightly between two point 50cm apart. It is plucked
at it centre and the velocity of the wave produced is 300ms-1.
Calculate the number of vibration made by the string in one second. Do
your working and don't forget to explain. Thanks.

[neuro]

(300 ms)^-1 or 300 ms^-1 (i.e. 300 kHz)?
not so tightly stretched in the first case, I would say, or maybe stretched a little too much in the second case?

:°)

I am no moderator here, but if this is a homework, you won't probably obtain an answer here.

If you wish to explain what is your technical or practical problem, what is your reasoning and why you cannot get the correct answer, then several people here may be able to help you.

[chikis]

Okay, for whoever wants to see my working:
Velocity, v of the spring = 300ms-1. Number of vibration is the same as the frequency, f which we are to find. The lengt of the string is the same as the wavelenght w = 50cm = (50/100)m = 0.5m,
using v = f(w)
f = v/w
f = 300/0.5
= 600Hz
but the answer I got is not the same with the one at the answer page of my book. I brought the problem in so that you guys can analyse it and tell whether am right or wrong. If am right, congratulate me and if am wrong, lead me and resolve the problem, then tell me where am wrong and correct me. Thank you.

[CanadysPeak]

Okay, for whoever wants to see my working:
Velocity, v of the spring = 300ms-1. Number of vibration is the same as the frequency, f which we are to find. The lengt of the string is the same as the wavelenght w = 50cm = (50/100)m = 0.5m,
using v = f(w)
f = v/w
f = 300/0.5
= 600Hz
but the answer I got is not the same with the one at the answer page of my book. I brought the problem in so that you guys can analyse it and tell whether am right or wrong. If am right, congratulate me and if am wrong, lead me and resolve the problem, then tell me where am wrong and correct me. Thank you.

"It is plucked at the center." What does that suggest to you? Beyond that, however, what on earth are you doing about the tuning? Get a guitar, try the exercise, think about the results.

[chikis]

When the string is plucked at it centre it will vibrate. The number of that vibration is equal to the frequency.

[CanadysPeak]

When the string is plucked at it centre it will vibrate. The number of that vibration is equal to the frequency.

Maybe, maybe not. Tell us a little about your background and what class you're taking. That will help in the explanation. Do you know, for example, about nodes and anti-nodes?

[chikis]

@CanadysPeak-
Am a secondary school leaver warming up for higher education.
I have heard about node and antinode, is just that I don't have a full knowledge about what is all about.

[CanadysPeak]

@CanadysPeak-
Am a secondary school leaver warming up for higher education.
I have heard about node and antinode, is just that I don't have a full knowledge about what is all about.

The two ends of the string will be stationary. The center will be plucked. IF the string vibrates, you will then have a node at each end and an antinode in the middle. You will thus have a half wave. You will have to double that length to get a full wave.

More importantly, however, is whether the string will even produce a standing wave. This will depend on the tension and the linear density of the string. Look at this link
http://hyperphysics.phy-astr.gsu.edu/hb ... tring.html

[chikis]

I think I have gotten the clue now. The lenght of the string, L = wavelenght,W/2
thus W = 2L
velocity, V = Frequency, F * W
using the relation with what I have:
F = V/ W
= V/2L
= 300m/2(50/100)m
= 300/1
= 300Hz
I hope am now on the right track?

[CanadysPeak]

I think I have gotten the clue now. The lenght of the string, L = wavelenght,W/2
thus W = 2L
velocity, V = Frequency, F * W
using the relation with what I have:
F = V/ W
= V/2L
= 300m/2(50/100)m
= 300/1
= 300Hz
I hope am now on the right track?

Does that agree with your book? Do the units come out correctly?

[chikis]

Actually the question is a multichoice question with option A-E. So am required to work and choose the option that correspond to my answer.
One of the option correspond to the answer that I got.

[neuro]

I must say I have been puzzled by your use of the term velocity since the beginning.
(I was initially mislead by your way of writing down units as well, as in my world ms^-1 means (milliseconds)^-1 and not m.s^-1 = meters/second).

The point is: what do you mean by velocity of a vibrating string? I initially though it was velocity=frequency=cycles/s (ms^-1 = kHz). Then - realizing my misreading units - I though it would mean the maximum velocity during the oscillation.

From your computation it appears that you refer to velocity as the longitudinal traveling velocity of a wave which reproduces the shape of the string during oscillation (i.e. wavelength = 2L) and displays the same lateral displacement (and lateral velocity) in time. Is this a standard way of defining "velocity" for the oscillation wave of a string?

[chikis]

Do we have more than one type of unit for velocity? The S.I unit for velocity which I knew right from when I began to study physics and that I have being using is is meter per second i.e m/s.
Please if they are other type, let me know.

[neuro]

I do agree with you that we have only one standard unit for linear velocity.
Still, I would appreciate your not being so rude, and trying instead to understand what I am asking.

The string vibrates.
Every point travels in space.
The speed of such travel changes at avery moment (and is maximum for the center point, zero at the limiting fixed points)
In particular, the speed sinusoidally varies with time, between a maximum speed in one direction (when crossing the middle point of the oscillation) and a maximum speed in the other direction (again when crossing the middle point).
This is velocity, linear velocity, meters/s, but it is an ACTUAL displacement velocity along the TRASVERSE axis of the string.
OK?

Then you can look at the string as if it where the representation of a wave that propagates.
Such a wave would have a wavelength twice the length of the string, because at each moment the string only "represents" half a wave.
Such a wave would also have an oscillation frequency (cycles/s = Hertz).
You can ABSTRACTLY think of a LINEAR VELOCITY of the wave, as given by the length travelled in one cycle (wavelength) multiplied by the number of cycles in a second (frequency).
NOTICE THAT THIS IS A LINEAR VELOCITY ALONG THE STRING (not transversally).

NOTHING MOVES LONGITUDINALLY AT THAT SPEED IN YOUR SYSTEM!!
Still, this is the way you seem to interpret speed:
I am not saying speed is something different from m/s, I am only asking whether in such a system it is standard convention to talk about velocity to mean the abstract linear speed of the wave ALONG the string, rather than the ACTUAL speed of the string (of the center-point of the string, not of the wave) TRANSVERSALLY with respect to the axis of the string.
Actually, I am not asking you this, but the engineers and physicists here

[CanadysPeak]

I do agree with you that we have only one standard unit for linear velocity.
Still, I would appreciate your not being so rude, and trying instead to understand what I am asking.

The string vibrates.
Every point travels in space.
The speed of such travel changes at avery moment (and is maximum for the center point, zero at the limiting fixed points)
In particular, the speed sinusoidally varies with time, between a maximum speed in one direction (when crossing the middle point of the oscillation) and a maximum speed in the other direction (again when crossing the middle point).
This is velocity, linear velocity, meters/s, but it is an ACTUAL displacement velocity along the TRASVERSE axis of the string.
OK?

Then you can look at the string as if it where the representation of a wave that propagates.
Such a wave would have a wavelength twice the length of the string, because at each moment the string only "represents" half a wave.
Such a wave would also have an oscillation frequency (cycles/s = Hertz).
You can ABSTRACTLY think of a LINEAR VELOCITY of the wave, as given by the length travelled in one cycle (wavelength) multiplied by the number of cycles in a second (frequency).
NOTICE THAT THIS IS A LINEAR VELOCITY ALONG THE STRING (not transversally).

NOTHING MOVES LONGITUDINALLY AT THAT SPEED IN YOUR SYSTEM!!
Still, this is the way you seem to interpret speed:
I am not saying speed is something different from m/s, I am only asking whether in such a system it is standard convention to talk about velocity to mean the abstract linear speed of the wave ALONG the string, rather than the ACTUAL speed of the string (of the center-point of the string, not of the wave) TRANSVERSALLY with respect to the axis of the string.
Actually, I am not asking you this, but the engineers and physicists here

In the case of a vibrating string, we usually refer to that longitudinal velocity as wave velocity. Few people at the apparent level of chikis ever consider the transverse velocity (even though its existence is essential for a standing wave to be present). I too often wind up simply using "soft" terms to match the student's use; I shouldn't, since failure to discriminate between the two principal velocities leads to difficulties in understanding simple harmonic motion.

[neuro]

thks, Canadys,
it's always good to learn something!

[chikis]

My heart is still runing round looking for commendation. I want somebody to approve or disapprove my last working as regards to the problem I used in starting this thread. By simply writing yes if approved and no if not. Or just by making statemement showing your approval or disapproval.

[CanadysPeak]

My heart is still runing round looking for commendation. I want somebody to approve or disapprove my last working as regards to the problem I used in starting this thread. By simply writing yes if approved and no if not. Or just by making statemement showing your approval or disapproval.

OK, I disapprove. You did not show your work, complete with formulas and a sketch. You did not use units consistently and properly. You did not indicate significant digits.

[chikis]

How can I show my work with skech when the question does not require that. Perhaps if am to represent my work with skech and send it in, I don't have a means to do that becuase I don't have a scanner. Where did I not use complete and consistent units? The number of vibration made by the string in one second is 300Hz. So where am wrong specifically? Qoute it out let me see.

[CanadysPeak]

How can I show my work with skech when the question does not require that. Perhaps if am to represent my work with skech and send it in, I don't have a means to do that becuase I don't have a scanner. Where did I not use complete and consistent units? The number of vibration made by the string in one second is 300Hz. So where am wrong specifically? Qoute it out let me see.

In your first post, you said, "Do your working and don't forget to explain." Did you forget?

[chikis]

Is that the type of skech you mean? If that is the type of skech you mean, don't worry, I will explain in my next post.