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

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Homework Help Overview

The discussion revolves around the effect of tension on the frequency of standing waves in a string, specifically examining how changes in tension influence the fundamental frequency of the string.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between tension and wave speed, with some questioning how to connect the concepts of tension and frequency. There is also a discussion about the relevance of specific equations and their derivations.

Discussion Status

Participants are actively engaging with the problem, with some offering equations and insights about the physics involved. There is a recognition of the need to guide understanding rather than simply providing answers. The original poster expresses a newfound understanding of the problem.

Contextual Notes

Some participants note the absence of certain formulas in the original poster's textbook, which raises questions about the resources available for solving the problem.

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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