A vibrating string vibrates at 100Hz in oxygen.What is the frequency of its vibration in Hydrogen?[assume same temperature and pressure]

Equating the velocities of sound gives 400Hz...But what pokes me is that the frequency is the property of the source.Will it change with ambient condition?
In other words should not the answer be still 100 Hz?

Nothing... depending, which frequency you are talking about?????

I am so00000000 sorry... I never read your question correctly.


It should be around 150HZ.

why?

Because it should be in-between, the same value.... if you get my meaning?

i do not understand your point

The point between two points......????? Atill get me?

i do not understand your point

I don't blame you. Reiku is the guy who thinks he has proved god through his studies of secret bible code mathematics. :rolleyes:

Can you proove me wrong?

I don't have to.

Oh, and, neelakash, I hope someone more competent helps you with your question soon.

Bye

Maybe.... just maybe... you can't?????

neelakash the frequency should remain the same

I think it should remain the same as well although it's possible that the duration of the vibration might be altered due to differing levels of friction with the atmosphere.

What would be different would be the sound wave which comes from the vibrating string. This is because of how the wave propagates through the medium. Example: helium.

The medium in the original post remains the same in different atmospheres: a string.

Just a guess though.

I don't blame you. Reiku is the guy who thinks he has proved god through his studies of secret bible code mathematics. :rolleyes:

Also...



.... the Bible Codes have been inspired. ;)

Both of you Nex + Draq are rigfht!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

neelakash the frequency should remain the same

Verry Well Said!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:eek::con fused::bugeye:

I also think that the frequency should be the same...But what is the logic behind it?The source???

Frequency, has a past, present and future clash, as showm in Dr Cramers Transactional Interpretation.

The source of the frequency is a vibrating string, which is set at a certain tension.

Variation in material properties will alter the frequency. The same can be said of the gas, but the damping ratio is too small to be accounted for in realistic situations. The gas serves as a viscous damper.
Vibration systems with viscous damping are governed by the differential equation

m[\ddot x]+c[\dot x]+k[x]=F_0cos(\omega t+\phi)

where the RHS is the forcing of the system and c is the damping constant, close to zero. There is no forcing in a free vibration of a string, so we can expect an ODE as such:

m[\ddot x]+k[x]=0

the [x] matrix is infinite, because in a string the mass is distributed. So this is an infinite DOF system.

The natural angular frequency of such an oscillation is

\omega_n=\sqrt{\frac{k}{m}},

where k is the spring constant and m is the mass of the oscillating body.
Now we see that E, the elastic modulus, has the definition

E=\frac{\sigma}{\epsilon},

where \sigma=\frac{F}{A}=\frac{-k \Delta L}{A} and \epsilon=\frac{\Delta L}{L_0}. So,

E=\frac{-k L_0}{A}. We assume the area is constant, which actually isn't true. Thus

k_{eq} =\frac{EA}{L_0}. Let us replace the mass with a mass distribution per unit length, or \frac{m}{L_0}. Also define the tension T = EA. In that case we end up with the same thing, or

\omega_n = \sqrt{\frac{T}{mL_0}}, or

f = \frac{1}{2\pi}\sqrt{\frac{T}{mL_0}}.

If you know the material density, then

f = \frac{1}{2\pi L_0} \sqrt{\frac{T}{\rho A}}

I typed this up w/o sources, so I might be wrong on this - someone needs to check my accuracy.

We should also note that the frequency of vibration is not necessarily the same as the audible pitch, since the latter depends on the speed of sound in that particular medium.

The audible pitch is the same as the frequency of the spring vibration. Otherwise, I think you're pretty close to right. The frequency should not be significantly affected by changing the surrounding atmosphere.

The audible pitch is the same as the frequency of the spring vibration. Otherwise, I think you're pretty close to right. The frequency should not be significantly affected by changing the surrounding atmosphere.
Kevinalm,
by audible pitch are you saying that a string vibrating at 400hz, for instance, will sound the same in mediums of air and helium? I would think that the difference in mediums (media?) would sound different due to the difference in the masses of the media striking the eardrum. Perhaps I am not in tune (pun intended) with "audible pitch"- please clarify.:shrug:

By pitch I mean the fundamental frequency, in other words the musical note. I think I see where your confusion comes from. We are all familiar with the 'sqeaky' voice you get from inhaling helium, or that drivers etc. get when on a special oxygen/helium mix for deep dives. But the human vocal apparatus is not a simple taunt string, vocal chords notwithstanding. The larynx is a resonent chamber somewhat like an organ pipe, and the entire larynx/vocal chord/vocal tract system is a strongly intacting closely coupled system. Helium does affect the resonance of the larynx/vocal tract which does strongly affect the frequency of vibration of the vocal chords, so the pitch goes up.

A simple taunt string however vibrates at a frequency determined almost entirely by it's linear mass density, the tension and the elasticity of the string. There may be a _very_ small effect due mostly to damping (wind resistance as the string moves) but it won't change the fundamental significantly.

Now that isn't to say that the shape of the waveform will be unchanged. The 'quality' of the sound may change but the pitch won't. (A violin and a saxophone may be playing the same note in the same octave, exactly the same pitch, but you can tell them apart.)

By pitch I mean the fundamental frequency, in other words the musical note. I think I see where your confusion comes from. We are all familiar with the 'sqeaky' voice you get from inhaling helium, or that drivers etc. get when on a special oxygen/helium mix for deep dives. But the human vocal apparatus is not a simple taunt string, vocal chords notwithstanding. The larynx is a resonent chamber somewhat like an organ pipe, and the entire larynx/vocal chord/vocal tract system is a strongly intacting closely coupled system. Helium does affect the resonance of the larynx/vocal tract which does strongly affect the frequency of vibration of the vocal chords, so the pitch goes up.

A simple taunt string however vibrates at a frequency determined almost entirely by it's linear mass density, the tension and the elasticity of the string. There may be a _very_ small effect due mostly to damping (wind resistance as the string moves) but it won't change the fundamental significantly.

Now that isn't to say that the shape of the waveform will be unchanged. The 'quality' of the sound may change but the pitch won't. (A violin and a saxophone may be playing the same note in the same octave, exactly the same pitch, but you can tell them apart.)

It would seem that stringing a guitar within a closed chamber at STP and then plucking the string, that when the pressure within the chamber is increased that the string will suffer measurable damping effects resulting in a decrease in frequency. Likewise, decreasing the pressure would have the effect of increasing the frequency, or so it would seem.

If we change the medium in the chamber from air to helium say, pluck the string and increase the pressure then would not a similar damping effect occur?

A 400 Hz sound wave generated from a helium medium that tightly encloses your right ear for instance will sound unique. Now let us tightly enclose the left ear and with air and and pluck a 400 Hz note there. Let us assume that the same numbers of medium, the surrounding gas, particles is the same #/x^3. Will not the sound be distinguishable by comparing the sound heard in both ears?

The frequency of both media is 400 Hz, yet the helium particles do not have as much drumming effect on the timpani of the ear as does the heavier oxygen. Now increasing the pressure in the left side while decreasing the pressure in the right side would have the effect of effecting the frequency, assuming pressure levels are significant.

When the saxophone and violin play simultaneously does not the interference of the sound waves have an effect of what is ultimately measured? Years ago I began playing an electric guitar and it became manifestly clear that two notes played together, or even close together had the quality of mixing in such a way that distinguishing the individual notes was not easily accomplished.

Further, when notes are played as a chord, three notes of any particular major scale for instance, that changing one of the notes and substituted with a comparable note from an other major scale will be heard as what is known as "flat" or perhaps "sharp", but most certainly dischordant.

Sound and vibrating strings are all effected by the physical effect klnown as resonance, where octave add one way and notes separated by nopte distance another way. Chords say a fifth within a major scale, while not mixing in resonance, there is nevertheless, mixing to a more energetic degree than notes from distance scale. Therefore, the damping effect of the medium must be considered as, possibly, including other emitted notes, which when adding positive cycle to positive cycle creates a distinct pressure difference that clearly effects the guitar motion and therefore the radiated sound.

An acoustical guitar string feels the reflected way from the back of the guitar which resonates with the plucked string, While the frequency of the string does not vary the sound from a cheap guitar is quite different from a well crafted guitar. That most guitar notes are multi-plucked means that the reverberation from the back of the guitar results is sounds clearly distinguishable from the 400 and say 500 Hz plucked strings played separately
:shrug:.

Most of your objections fall under what I called 'sound quality'. A 400hz square wave and a 400hz sine wave are the same note. To the ear, they are easily distinguished but they are also the same 400hz note or pitch. (The difference is that a square wave is rich in odd order harmonics, 3f,5f,7f...) The point I was originally making is that if something is emitting a 400hz tone, the ear will perceive it as a 400hz tone no matter what the atmosphere. A simple string without a resonant cavity attached will not change its frequency (at least not significantly) just because it is emersed in a helium atmosphere. Yes the harmonic content may be altered (which is equivalent to saying that the waveform may be altered) but that doesn't change the fundamental frequency.

The audible pitch is the same as the frequency of the spring vibration. Otherwise, I think you're pretty close to right. The frequency should not be significantly affected by changing the surrounding atmosphere.

Ah yes, that's right - I had the wrong picture in mind.

Sometimes I am too visual, which leads to the wrong conclusion. Indeed the audible frequency will be the frequency of vibration.

Ok, I just spotted another error -

T is not equal to EA. I'm really getting my definitions mixed up.

So the equation is really supposed to be

f=\frac{1}{2 \pi L_0}\sqrt{\frac{E}{\rho}}