How does tension affect the frequency of a standing wave on a string?

AI Thread Summary
Tension in a string significantly affects the speed of sound within it, thereby influencing the frequency of standing waves. When the tension is doubled, the fundamental frequency increases, with the new frequency calculated to be 354 Hz. The relevant equation for understanding this relationship is v = (F/(ρ⋅A))^(1/2), where F represents tension, ρ is the string's density, and A is its cross-sectional area. Participants in the discussion emphasized the importance of problem-solving skills in physics rather than merely applying formulas. Overall, the conversation highlighted the connection between tension and wave frequency while addressing the learning process in physics.
sushichan
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Homework Statement


A string is held under tension, with both ends fixed, and has a fundamental frequency of 250 Hz. If the tension is doubled, what will the new frequency of the fundamental mode be?

Homework Equations



The Attempt at a Solution


I don't know how tension can affect the equation v=ƒλ. I re-read the chapter twice still couldn't find it.(Ans: 354 Hz)
 
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Hello Sushi, welcome to PF :smile: !

Perhaps you can google "vibrating string" ?
 
According to my physics book, the tension affects the speed of sound in the string.
A useful equation is: v = (F/(ρ⋅A))^(1/2)
where F = tension
ρ = density of string
A = cross section area of string :)
 
Looks good to me ! Even better: it matches what one finds, e.g. here

Hey, wait a minute ! We're supposed to help folks find the answers by themselves, not just dump them on a plate !
 
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BvU said:
Hey, wait a minute ! We're supposed to help folks find the answers by themselves, not just dump them on a plate !

I'm sorry, but my jugment was simply that revealing a, for the asker unknown, equation was a way to help him/her in solving the actual problem.
In my opinion it might be hard to know what to search for without knowing what you look for. And physics is after all about problem solving and not google-searching skills, at least it is for me.

However, I'm sorry and will do my best to avoid helping people like this in the future! :)
 
Alettix said:
According to my physics book, the tension affects the speed of sound in the string.
A useful equation is: v = (F/(ρ⋅A))^(1/2)
where F = tension
ρ = density of string
A = cross section area of string :)
What is the derivation of it?
Simply putting values in a formula is not physics.
Although it is OP duty to ask meaning of an equation,
But interest is developed in young guys when one explains them in a proper way.
 
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Thank you all, I know how to solve it now ^^

It's just funny I don't see this formula in the textbook.
 

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