# Soundvelocity dependence on temperature?

1. Jan 9, 2009

### JANm

It is cold outside, inside too but thats of no importance to the matter.
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?

2. Jan 9, 2009

### atyy

I don't know the equations behind this, but some practical stuff around a 10 degree C range (20-30 degree C). A pipe organ will operate ok over that range (assuming only relative pitch matters, absolute pitch will not be ok). However, for each temperature, the organ must come to equilibrium (about one hour), otherwise it will sound out of tune.

3. Jan 9, 2009

### JANm

Does that mean difference of temperature in the brass or wood of the pipes? Is that hour necessary for equalisation of these temperatures? For actually my question is about the temperature of the gas...

4. Jan 9, 2009

### FredGarvin

In the most simplistic form, the speed of sound in an ideal gas, c, can be estimated via:

$$c = \sqrt{\gamma*R*T}$$

where
$$\gamma$$ = Ratio of specific heats
$$R$$= Ideal gas constant
$$T$$ = Absolute temperature

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

$$c =\sqrt{\frac{B}{\rho}}$$

where
$$B$$= the material's bulk modulus (a measure of it's stiffness)
$$\rho$$ = 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.

5. Jan 9, 2009

### atyy

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

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

6. Jan 10, 2009

### JANm

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.

7. Jan 10, 2009

### LURCH

yes, this changes the velocity of the sound, but does not effect the pitch. If your instrument is egnerating 440 Hz, then that is the pitch that will propagate through the air. Changes in the pitch of musical instruments on cold days (I used to be in a marching band) caused by the expansion or contraction of the instrument itself, not by the change in velocity of sound wave propagation.

8. Jan 10, 2009

### JANm

Sorry, someway I should have known. So the frequency of an instrument is not dependent on the velocity of sound. And the frequency of an instrument, for instance the piano contraction of the snares, or rather tension in the snares. But for the organ pipes? If there are different temperature layers of air in these pipes?

9. Jan 11, 2009

### Shackleford

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.

10. Jan 11, 2009

### JANm

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?

11. Jan 11, 2009

### Shackleford

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.

12. Jan 11, 2009

### JANm

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.