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Author Topic: Why does thinner metal have a higher pitch?  (Read 2451 times)

Ananya Raman

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Why does thinner metal have a higher pitch?
« on: 29/09/2009 11:30:03 »
Ananya Raman  asked the Naked Scientists:
   
Hi!

I made a drum out of a coffee tin. Then, I drew a line a third of the way on the base, and hammered down on the line so that part was thinner. There is a higher pitch on the side I hammered and I think it has something to do with there being less particles for it to travel through (?) but I'm not too sure.

Can you please explain to me how the pitch was changed in scientific terms? (And also practical terms in another paragraph/sentence?)
 
Thank you so SO much! This is just something that I have been thinking about since I made the drum. It is actually for a school project, and I need to know how the pitch is changed in scientific and practical terms! Please help me!
 
THANK YOU!!
 
-Ananya

What do you think?


 

Offline Vern

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Why does thinner metal have a higher pitch?
« Reply #1 on: 29/09/2009 21:19:31 »
The thin place has less mass to move as it vibrates. Less mass makes its natural resonant frequency higher so the higher pitch.
 

Offline daveshorts

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Why does thinner metal have a higher pitch?
« Reply #2 on: 02/10/2009 14:58:53 »
I don't know if it is just that it is thinner. If you make a sheet of metal thinner it will get lighter per unit area which will increase the pitch. However it will also make the metal more flexible, and stiffness is proportional to the cube of the depth of a beam, so it will get a lot less stiff. A reduction in stiffness will reduce the pitch, and the reduction due to stiffness will be more than the increase due to it getting lighter.

Basically if the drum was a string (it isn't and is therefore more complex) the frequency of vibration and therefore the pitch is proportional to the square root of (the stiffness/the mass per unit length), More mass means that a object will take longer to accelerate -> lower speed of vibration. More stiffness means that the forces will be larger for the same displacement -> higher accelerations -> higher speed of vibration.

When you hammer you probably also make it more curved. Making it more curved (particularly in 2 directions) will make it stiffer without making it more massive so the pitch will go up. This is why cars don't have flat panels, the steel they are made from would be quite floppy if it wasn't curved.

But saying that the physics of musical instruments is always more complex than one thinks...
 

Offline Vern

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Why does thinner metal have a higher pitch?
« Reply #3 on: 03/10/2009 20:21:22 »
Your analysis looks good to me.
 

Offline chris

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Why does thinner metal have a higher pitch?
« Reply #4 on: 10/10/2009 09:39:56 »
I don't know if it is just that it is thinner. If you make a sheet of metal thinner it will get lighter per unit area which will increase the pitch. However it will also make the metal more flexible, and stiffness is proportional to the cube of the depth of a beam, so it will get a lot less stiff. A reduction in stiffness will reduce the pitch, and the reduction due to stiffness will be more than the increase due to it getting lighter.

Basically if the drum was a string (it isn't and is therefore more complex) the frequency of vibration and therefore the pitch is proportional to the square root of (the stiffness/the mass per unit length), More mass means that a object will take longer to accelerate -> lower speed of vibration. More stiffness means that the forces will be larger for the same displacement -> higher accelerations -> higher speed of vibration.

When you hammer you probably also make it more curved. Making it more curved (particularly in 2 directions) will make it stiffer without making it more massive so the pitch will go up. This is why cars don't have flat panels, the steel they are made from would be quite floppy if it wasn't curved.

But saying that the physics of musical instruments is always more complex than one thinks...

That is an amazing answer. Thanks Dave.

c
 

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Why does thinner metal have a higher pitch?
« Reply #4 on: 10/10/2009 09:39:56 »

 

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