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I have seen the formula of velocity of sound dependent on pressure and density. Can that in some way be translated to dependence on temperature? Do musical instruments have to be "calibrated" if played in extreme colds?

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- Thread starter JANm
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I have seen the formula of velocity of sound dependent on pressure and density. Can that in some way be translated to dependence on temperature? Do musical instruments have to be "calibrated" if played in extreme colds?

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atyy

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FredGarvin

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[tex]c = \sqrt{\gamma*R*T}[/tex]

where

[tex]\gamma[/tex] = Ratio of specific heats

[tex]R[/tex]= Ideal gas constant

[tex]T[/tex] = Absolute temperature

For some other material that is not an ideal gas, say, water, you need to look at the following

[tex]c =\sqrt{\frac{B}{\rho}}[/tex]

where

[tex]B[/tex]= the material's bulk modulus (a measure of it's stiffness)

[tex]\rho[/tex] = the material density

As far as the instruments go, it depends on what kind of instrument you are talking about. Most common instruments are tuned every time you play them and also during play simply because of so many factors. Large instruments like pipe organs and pianos are tuned once and usually you don't see them move to varying environments.

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atyy

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Have no idea, I would think wood, brass and gas (since the boundary conditions also determine the pitch).

Large instruments like pipe organs and pianos are tuned once and usually you don't see them move to varying environments.

Yes, but just in case anyone's wondering, the case I was talking about was air conditioning in the "summer".

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Thanks for this formula. So the 20-30 temperature range with 10 change is about 3% of the absolute temperature, and gives 1,5 % change in soundvelocity because of the square root.[tex]c = \sqrt{\gamma*R*T}[/tex]

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LURCH

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Well, if you're talking about the sound waves produced from, say, a piano, then the frequency of the sound waves is determined by the vibration of the strings, and it is of course the same vibration that moves that air molecules. The frequency in the string, of course, is based on the tension and mass per unit length. The wavelengths are different, though, because the velocities of the waves are different. Velocity is dependent upon the medium in which the wave travels.

In open or closed pipes or other enclosures, the sound waves are determined by the standing waves that can be produced within that particular structure. It's easily calculable in pipes, of course. If there is a very noticeable difference in air temperature in a pipe, then that would have an affect on the standing wave possible.

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In open or closed pipes or other enclosures, the sound waves are determined by the standing waves that can be produced within that particular structure. It's easily calculable in pipes, of course. If there is a very noticeable difference in air temperature in a pipe, then that would have an affect on the standing wave possible.

From the largest textbook I have ever owned (Kronig) have I remembered that the median velocity of the molecules is sqrt(3)*c. Is the standing wave in an organ pipe dependent on the median velocity or rather the fastest molecules?

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From the largest textbook I have ever owned (Kronig) have I remembered that the median velocity of the molecules is sqrt(3)*c. Is the standing wave in an organ pipe dependent on the median velocity or rather the fastest molecules?

Well, I'm not really sure. I don't think that was covered in my textbook, but I would have to look. Offhand, I'd say the median velocity. As time goes on, thermal energy is being passed from hotter air to cooler air as to reach thermal equilibrium. Also, it would depend on the temperature difference, too. The difference could be highly negligible until you reach a certain difference.

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As time goes on, thermal energy is being passed from hotter air to cooler air as to reach thermal equilibrium. Also, it would depend on the temperature difference, too.

OK let us remain bij the 10 degree difference, regardless of it being a summer example and the most stable situation the hot air above the cold air in 50-50 abundance. In meteorology this is called an inversion. I don't know so much about organs* but some of the cold air with soundvelocity 1 mach is blown to the hot air with soundvelocity 1,015 mach.

In what way is the frequency different from the mixed air?

*found the formula for the basetone f_0=c/(2*l)

where c is soundvelocity and l length of the pipe. If the end of the pipe is covered the frequency is halved f=f_0/2 and at 1/3 of the closed end a third harmonic f=3 f_0 is reached.

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