How Do Wire Characteristics Affect the Notes They Emit?

[Abhishekdas]

Homework Statement

The lengths of two wires are in the ratio 1:2, their tensions are in the ratio 1:2 and their diameters in the ratio 1:3 . The ratio of the notes they emit when sounded together by the same source is?

Homework Equations

The Attempt at a Solution

How to do this problem...What exactly are notes...A google search didnt help much...

 

[Redbelly98]

"Notes" means a musicalnote, that is the frequency of the sound emitted by a vibrating wire. Your textbook should have a discussion, and relevant equations that involve quantities mentioned in the problem statement (tension, wire length).

 

[Abhishekdas]

Ok...so notes are simply their frequencies?
ok if so then i am assuming both wires to be of the same material...I have velocity given by √(T/density*A) ...here T = tension , A=cross sectional area...Now i have the ratio of their velocities...But if i want to use f=v/wavelegth i don't have wavelength...SO how do i go about it? and does the length of the wires play any role?

Thank you for your reply...

 

[Redbelly98]

Yes, the notes are the frequencies. And yes, the length of wire plays a role in the wavelength; the wavelength is determined by the length of the wire. (There is probably a figure showing this in your textbook or lecture notes.)

 

[Abhishekdas]

Are you talking about the concept of standing waves where the length is an integral multiple of (wavelength/2). In this case they are not talking about any particular frequency (fundamental or 2nd overtone 3rd overtone whatever...)...So how do i get the wavelength?

 

[Abhishekdas]

And what is the significance of saying that they are from the same source?

 

[Redbelly98]

The note is the frequency of the fundamental. I'm not sure what the "same source" refers to.

 

[Abhishekdas]

Ok...i got it using the fact that notes is corresponding to the fundamental frequency...Thanks...