# Variation of the Speed of Sound in metals under tension

• I
Summary:
In a block of metal, each metal has a characteristic speed of sound. When metal is under tension, such as a guitar string, the speed rises as the tension increases. How does the speed vary (in a block say) as a function of tension along each of the three axes? I am assuming that transverse tension has some effect on velocity.
In a block of metal, each metal has a characteristic speed of sound. When metal is under tension, such as a guitar string, the speed rises as the tension increases. How does the speed vary (in a block say) as a function of tension along each of the three axes? I am assuming that transverse tension has some effect on velocity.

## Answers and Replies

Baluncore
Science Advisor
When metal is under tension, such as a guitar string, the speed rises as the tension increases.
The speed of sound remains reasonably constant with changes in tension or compression.

It is the frequency of string oscillation that rises, not the speed of sound.

While the mass of the string remains constant, the transverse restoring force is increased with tension in the string. The frequency of oscillation therefore rises.

The speed of sound remains reasonably constant with changes in tension or compression.

It is the frequency of string oscillation that rises, not the speed of sound.

While the mass of the string remains constant, the transverse restoring force is increased with tension in the string. The frequency of oscillation therefore rises.
OK, thank you for that insight.

So please leave aside my mistake here. Does the speed of sound vary with tension, even only slightly? And does it rise when there is a transverse tension?

Baluncore
Science Advisor
Does the speed of sound vary with tension, even only slightly?
Not really. The elasticity of metals tend to be linear below the yield point when plastic deformation begins. Where the density is stable and Young's Modulus is stable, the speed of sound will remain stable.
https://en.wikipedia.org/wiki/Young's_modulus
Notice there is some temperature dependence.
The speed of sound will change due to changes in density, which may be changed slightly, by a couple of percent, due to tension or compression.

sophiecentaur
Science Advisor
Gold Member
2020 Award
It is the frequency of string oscillation that rises, not the speed of sound.
This link shows that wave speed and frequency are both functions of tension.
That's in the the case of a normal transverse wave but speed of sound in bulk steel is much higher; the modulus is much higher. But I would suggest that the case of a longitudinal wave on a string would be somewhere in between. As a section of string is compressed or stretched, its volume can change (no steel either side to contain it) so you would have surface waves ("string of beads") travelling along the string. Much faster than regular waves on a string but much slower than regular compression waves in bulk steel.

I can't see how the speed of a bulk wave in a linear, isotropic solid would be affected by tension but a longitudinal wave on a steel string wouldn't necessarily be as straightforward because of the transverse component along the surface.

Thanks for the replies. Where I am trying to get to with my line of questions is somewhere else entirely, but I couldn't start there because there is too much baggage in the history. I am looking at electromagnetism as being the waves of an aether which was how it started out but people got all silly about M-M experiment disproving the aether which it did not.

It seems to me that if the fundamental equations of the Universe are the equations of motion of a tensile medium (aether) and there is some non-linearity due to the stretching of the medium then it is possible to derive GR from that. But how to get started with the right equations is the problem.

Based on a non-linearity in the aether equations it is possible to explain the entire structure of the Universe and predict the scale of different structures from Hubble scale to galaxies, stars, planets, moons, ... cells, atoms, nucleons, (quarks?) these all being near ratios of 34560 or about 10^4.5.

Baluncore
Science Advisor
But how to get started with the right equations is the problem.
First study a Physics degree.
Then you will be in a position to evaluate the possibilities.
Explore the field of accepted physics before inventing a parallel field.

Be aware of the Dunning-Krugger Effect.
https://en.wikipedia.org/wiki/Dunning–Kruger_effect

• • sophiecentaur and hutchphd
sophiecentaur
Science Advisor
Gold Member
2020 Award
Be aware of the Dunning-Krugger Effect.
. . . .where angels fear to tread?

First study a Physics degree.
Then you will be in a position to evaluate the possibilities.
Explore the field of accepted physics before inventing a parallel field.

Be aware of the Dunning-Krugger Effect.
https://en.wikipedia.org/wiki/Dunning–Kruger_effect
I did study physics about half a century ago.

I have developed a theory which explains many previously unexplained observations. It has also made several predictions that have been verified. It is vastly more successful that the Big Bang theory.

Some examples. There are many more.
* In the mid 1990s I calculated Hubble constant as 71.2km/s/Mpc which is still the best estimate.
* Also in 1994I predicted a particle of mass 34.76 Mev and it was discovered in 1995 with mass 33.9 Mev. A far better accuracy than Higgs Boson predictions.
* I have explained the 72 km/s redshift periodicty (wrongly called quantum) and other similar periodicities that have been confirmed by every properly conducted study, and which continue to be ignored by mainstream cosmology because it proves them wrong. Tell them about Dunning-Kruger.

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• • weirdoguy, davenn and Motore
Not really. The elasticity of metals tend to be linear below the yield point when plastic deformation begins. Where the density is stable and Young's Modulus is stable, the speed of sound will remain stable.
https://en.wikipedia.org/wiki/Young's_modulus
Notice there is some temperature dependence.
The speed of sound will change due to changes in density, which may be changed slightly, by a couple of percent, due to tension or compression.
I am aware of temperature variation. Do I take your last sentence to mean that the "not really" at the start means "not by much"?

Baluncore
Science Advisor
I can only guess. Your details do not list your level of education in physics.
The Physics Forum is not the place to develop or expound private theories.

Does the speed of sound vary with tension, even only slightly?

Not really. The elasticity of metals tend to be linear below the yield point when plastic deformation begins.
Do I take your last sentence to mean that the "not really" at the start means "not by much"?
If you compress a metal and the density increases, then you can expect a slight change in the speed of sound. In the same way, shock waves in a gas travel at a speed greater than the speed of sound.

When the material compression reaches the yield point, energy will be lost in plastic deformation, so cannot be recovered on elastic relaxation. The yield point can be reached by a static pressure plus the sound wave pressure, the material then becomes non-linear.

Pattern matching the mathematics of physical analogies is not the best way to advance a concept. The points where the theories break down will be different in each case.

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hutchphd
Science Advisor
Homework Helper
But how to get started with the right equations is the problem.

Yep. We can all agree that will be a problem.

I was mistaken when I was seeking a variation in speed of sound in metals with tension. Thanks for clearing that up.

I think that for my purposes a better example would be a cubic lattice of springs or wires. In that case, variations in tension due to stretching would vary the wave propagation wouldn't it?

What I then want to know is whether transverse stretching (to the direction of waves that we are considering) would also vary the speed of waves?

Thanks to everyone for their help. I am not wanting to discuss my theory here. I am trying to get a parallel situation that has the necessary qualities.

hutchphd
Science Advisor
Homework Helper
This will take you into the realm of nonlinear wave equations. You are correct to worry that the presence of the transverse wave on a string will slightly change the tension but in most circumstance these effects are small enough to be ignored. They also lead rapidly to very difficult mathematical solutions. Usually not worth the effort.
A more interesting thing to worry about is dispersion: where the speed of the wave depends upon wavelength. The maths are somewhat less difficult.

This will take you into the realm of nonlinear wave equations. You are correct to worry that the presence of the transverse wave on a string will slightly change the tension but in most circumstance these effects are small enough to be ignored. They also lead rapidly to very difficult mathematical solutions. Usually not worth the effort.
A more interesting thing to worry about is dispersion: where the speed of the wave depends upon wavelength. The maths are somewhat less difficult.
Yes, I know that what I seek is non-linear wave equations. All the predictive results that I have depend on that being true. The effects may well be small, but cannot be ignored.They are the whole point of the exercise.

There are also rotational effects in the medium that make things very complicated. In Maxwell's equations, there is a reason that one operator is called "rot". Electric and magnetic fields can be understood as velocity and rotation of a tensile aether. Particles can be understood as a type of standing wave in the aether or e/m fields. I recommend the work of Milo Wolffe who proved that a wave structure with spherical rotation (check that out) has exactly the properties of an electron. Other particles are more difficult.

For now I am ignoring wavelength affecting speed of propagation, but it is a possibility.

hutchphd
Science Advisor
Homework Helper
Of course none of this is new physics. It has been the mainstay of solid state (condensed matter) physics for at least a century, and much very elegant work has been done. I advise you to learn all that is extant.

sophiecentaur
Science Advisor
Gold Member
2020 Award
Particles can be understood as a type of standing wave in the aether
Do you have any evidence of measurements that support this? You seem to be just assuming this is a good model but have your ideas been peer reviewed? PF has to treat your ideas with the same reservations as many totally crackpot ideas because that's the policy and the purpose of PF is to limit discussion to established Physics.

DrClaude
Mentor
I have developed a theory which explains many previously unexplained observations. It has also made several predictions that have been verified. It is vastly more successful that the Big Bang theory.
We do not discuss personal theories here. Thread closed.

• hutchphd