Cold air and sound..

[instromp]

I remember a couple of days ago it was very cold one morning,and the school bell's pitch is normally g-natural.But it was different, it was g-sharp that day,i kno that when its raining pitch normally tends to be flat,etc.Since rainy days make the piano sound flat,does cold weather make it sound sharp I have been pondering about this lately

[henrah]

Do you have perfect pitch?

[instromp]

Do you have perfect pitch?

No,i wish i did . I knew the pitch because a piece of music i kno starts on g-sharp so i hummed the bell's pitch and knew it was sharped.

[asyncopated]

It's unlikely that it is the temperature of the air itself the made that pitch of your school bell higher.  Although temperature air does affact the density of air, and hence the pitch, it is very unlikely that it would change by a whole semitone.  Otherwise everyone will be speaking with a higher voice when it gets cold.

However, there are a lot of instruments that are sensitive to temperature.  You will see violinist keeping their instruments under their jackets if they have to play in cold temperature. 

This is for two reasons.  The wood does not like large changes in temperature.  This goes for all instruments, including pianos.  And secondly the metallic strings do contract enough to raise the pitch in a tangible way.  I don't know how your school bell was made (material/shape), but i think it's unlikely the same contraction cause the bell to deform enough to change its pitch.   

The pitch of the bell is determined by a two dimensional area (solving the helmholtz equation if you really want to know) rather than a string which is one dimensional, so it is less sensity of expansion and contraction.

So in the end, I'm not sure why the pitch changed.   Go steal the bell, and try to find out!

[instromp]

It's unlikely that it is the temperature of the air itself the made that pitch of your school bell higher.  Although temperature air does affact the density of air, and hence the pitch, it is very unlikely that it would change by a whole semitone.  Otherwise everyone will be speaking with a higher voice when it gets cold.

However, there are a lot of instruments that are sensitive to temperature.  You will see violinist keeping their instruments under their jackets if they have to play in cold temperature. 

This is for two reasons.  The wood does not like large changes in temperature.  This goes for all instruments, including pianos.  And secondly the metallic strings do contract enough to raise the pitch in a tangible way.  I don't know how your school bell was made (material/shape), but i think it's unlikely the same contraction cause the bell to deform enough to change its pitch.   

The pitch of the bell is determined by a two dimensional area (solving the helmholtz equation if you really want to know) rather than a string which is one dimensional, so it is less sensity of expansion and contraction.

So in the end, I'm not sure why the pitch changed.   Go steal the bell, and try to find out!

It's not an oldfashioned school bell that's metal, its electronic that sounds over the P.A. when its time to go to class.But we do speak in a higher voice when its cold(well i kno i do), because i know for a fact that when its cold, people's voices sound nasal like and higher,that could be a possibility.But anyway, its still a mystery to me though on why it was g-sharp eventhough you said cold temperatures make the air denser and affects pitch.I will have to experiment with this more.When i go back to school Monday(no school tomorrow,three day weekend,yaye ) i will listen to see if the bell's natural pitch is back to normal.

[ksnmohan]

Not just the Temperature - humidity and direction/speed of the wind/breeze also contribute each in its own way in making the sound to be heard different.

Being an "electrical bell" hooked to a PA, there cannot be any change on that part of the sound creation.

[timothy42b]

Wind instruments are strongly affected by temperature.   This is because the speed of sound is pretty much solely determined by the temperature of the air.  If it takes a sound wave longer to get to the end of the tube, because it is going slower in cold air, then that is the same as making the tube longer.  So a cold flute or trombone will always play flat. 

Other instruments are much less affected.  I can't imagine a bell changing much, whether mechanical or electronic.  I suggest checking this out with an electronic tuner to be sure what you're hearing is accurate. 

[asyncopated]

Thinking about it, temperature does cause the pitch to change.  Here are some calculations just for fun to show you why.  Say in summer it's about 25 degrees C and winter about 5 degrees C, outdoors

In this case the speed of sound according to https://en.wikipedia.org/wiki/Speed_of_sound (which i assume to be true) is

346.34 m/s in the summer and
334.52 m/s in the winter

Let there be a flute that produces produces a perfect A in the summer at 440 Hz.

The wavelength is thus 346.34/440 = 78.71 cm.  The position of the hole is actually a quater of this wavelength as the flute is an open ended instrument.

Since the length of the instrument can't change, in winter, it produces a note that is
334.52/0.7871=425 Hz.

If you look at this https://www.phy.mtu.edu/~suits/notefreqs.html,  we see that a g# is about 415 Hz, so it droped almost, but not quite a semitone. 

Here is the funny thing.  Colder temperature should cause the pitch to fall not to go up, and this is provided it comes from an instrument of fixed lenght.  Not to sure about electronic bells.

So i still can't understand why you heard the pitch go up instead of down.
 

[instromp]

Thinking about it, temperature does cause the pitch to change.  Here are some calculations just for fun to show you why.  Say in summer it's about 25 degrees C and winter about 5 degrees C, outdoors

In this case the speed of sound according to https://en.wikipedia.org/wiki/Speed_of_sound (which i assume to be true) is

346.34 m/s in the summer and
334.52 m/s in the winter

Let there be a flute that produces produces a perfect A in the summer at 440 Hz.

The wavelength is thus 346.34/440 = 78.71 cm.  The position of the hole is actually a quater of this wavelength as the flute is an open ended instrument.

Since the length of the instrument can't change, in winter, it produces a note that is
334.52/0.7871=425 Hz.

If you look at this https://www.phy.mtu.edu/~suits/notefreqs.html,  we see that a g# is about 415 Hz, so it droped almost, but not quite a semitone. 

Here is the funny thing.  Colder temperature should cause the pitch to fall not to go up, and this is provided it comes from an instrument of fixed lenght.  Not to sure about electronic bells.

So i still can't understand why you heard the pitch go up instead of down.
 

I still cant understand why it went up instead of going down either,very wierd.

[ksnmohan]

Asyncopated's explanation is perfect - but for the conclusion.

Since the length of the instrument (flute) does not change (as well as the blowing power/ method/sytyle of the Fautist), at the flute's end a 440 Hz wave form is still produced at a perfect "A".

This is the Frequency at GENERATION.

But the wave lengths in  TRAMSMISSION are

In Summer at 346.34 m/s  is 346.43 divided by 440 = 78.71 cm
In Winter at 334.52 m/s iis 334.52 divided by 440    = 76.02 cm

A smaller Wave length (in Winter) means a higher frequency or higher pitch - this time merely on account of the  TRANSMISSION.

The note will sound higher - hence the pitch going up. Irrespective of Acoustic or Electronic sources of the Sound Generation.

Not at all wierd!

Prof K S Narayanan

[asyncopated]

Asyncopated's explanation is perfect - but for the conclusion.

Since the length of the instrument (flute) does not change (as well as the blowing power/ method/sytyle of the Fautist), at the flute's end a 440 Hz wave form is still produced at a perfect "A".

This is the Frequency at GENERATION.

But the wave lengths in  TRAMSMISSION are

In Summer at 346.34 m/s  is 346.43 divided by 440 = 78.71 cm
In Winter at 334.52 m/s iis 334.52 divided by 440    = 76.02 cm

A smaller Wave length (in Winter) means a higher frequency or higher pitch - this time merely on account of the  TRANSMISSION.

I beg to differ here.  It's the wavelenght that remains the same not the frequency.  The wavelenght is determined by the distance from the mouthpiece to the hole that releases the note.  I don't recall a flute manually or automatically changing it's lenght (but I'm not neither a flutist nor a flautist), so we need someone who is willing to play the flute in the cold to corroborate the theory.

Anyway, what I say is consistent with what timothy said

So a cold flute or trombone will always play flat.

Btw, for an instrument, or a speaker that generates a consistent 440 Hz, despite the temperature, that wavelength does change but the note remains the same.

This is because you hear the note by hairs in your cochlear vibrating (moving to and fro).  This reponds to frequency rather than wavelenght.  So a speaker producing an A, vibrating at 440Hz in the summer or in the winter should still sound like an A.
https://en.wikipedia.org/wiki/Cochlea

[timothy42b]

The note will sound higher - hence the pitch going up. Irrespective of Acoustic or Electronic sources of the Sound Generation.

Not at all wierd!

Prof K S Narayanan

No.  I am a trombone player, and frequently do the tuning for mixed groups I play with.  I can tell you definitely cold instruments play flat and go sharp as they warm up.  Every wind instrument player has experienced this.  I'm also an engineer and can tell you the wave speed is slower in cold air, that makes the tube longer.  I'll show you the math if you insist. 

[ksnmohan]

Hallo Timothy,

Agree. Metal instruments - like the trombone and flute - tend to sound sharper when they warm up. But this is not the case with ALL instruments.
 
Here is, reproduced from another Forum, a discussion on the subject:

Started by
Christina K,  Student,  Age 14

Question -   I am just wondering why temperature effects how a musical instrument sounds.

My band teacher told me that depending on the temperature, the sound can go SHARP OR FLAT (the caps are mine)


One pertinent reply is from
 
Dr. Ken Mellendorf
Physics Professor
Illinois Central College

"Hi Christina -

Temperature affects lots of physical things. And musical instruments are tuned pretty precisely.

Instruments change differently by temperature.

On a steel-stringed wood guitar, warming makes the wood get longer, but the steel does not change nearly as much.   So the string is stretched tighter, and its vibrating frequency goes up (My comment: MEANS SHARPER WHEN WARM -so, same as the Trombone).

On a nylon-stringed wood guitar, the nylon expands and sags even more than wood, so the pitch goes DOWN with HEAT (agin, the Caps are mine).

Only a violinist would know what the violin does (My comment: I have a violin student and here in Chennai (South India) when she goes for a performance straight into an air-conditioned Auditorium (20 Degrees C) from an external (normal!) 35 degrees C,  the metal strings shrink faster than the wood and hence sound SHARPER with cold - viz more Flat with heat) 

A metal flute will go sharper when hot, because the speed of sound in air goes as the square-root of temperature. I can calculate this one: changing from 60F to 80F, our temperature above absolute cold increases about 4%, so sound goes 2% faster, so the pitch at 80F will be 1/3 of a note higher than at 60F."

So, there doesn't seem to be an universal rule.

Anyhow, we are having a nice discussion!

Prof K S (Mohan) Narayanan

[timothy42b]

A metal flute will go sharper when hot, because the speed of sound in air goes as the square-root of temperature. I can calculate this one: changing from 60F to 80F, our temperature above absolute cold increases about 4%, so sound goes 2% faster, so the pitch at 80F will be 1/3 of a note higher than at 60F."

So, there doesn't seem to be an universal rule.

Anyhow, we are having a nice discussion!

Prof K S (Mohan) Narayanan

Yes, now I can agree with you.  Instruments that depend on the speed of sound in air (tube length type instruments) should always go flat in the cold.  Instruments that depend on string tension might go either way.  Instruments that depend on the mass and stiffness characteristic, such as a bell, are unlikely to change at all. 

The temperature gradient can have an interesting effect.  If the room air is cold, the instrument will warm slowly spreading from the player's mouth and hands down the instrument.  So it may be much warmer at one end than the other.  The air enters at body temperature but moves very slowly down the tube and is cooled off as it goes.  A wood flute will warm very slowly as heat transmission in wood is slow.  The metal flute next to it will warm much more quickly.  If you tune them both when cold, very soon they'll be out of tune again. 

Temperature can affect electronic circuits by changing the resistance of components.  This is the reason so much effort goes into temperature compensation circuits and software for items like watches.