How Does Doubling the Tension Affect the Frequency of a Vibrating Wire?

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Homework Help Overview

The discussion revolves around the relationship between tension and frequency in a vibrating wire, specifically examining how doubling the tension affects the frequency of a 2-meter long wire that initially vibrates at 330 Hz under a tension of 500 N.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the wave propagation speed in the wire and the formula relating frequency to tension. Questions arise regarding the determination of mass density and its relevance in the context of the problem.

Discussion Status

Some participants have suggested that the frequency is proportional to the square root of the tension, indicating a potential direction for understanding the relationship. There is an ongoing exploration of the implications of constant variables such as length and mass density.

Contextual Notes

Participants are considering the assumption that the wire's properties remain unchanged when tension is altered, which raises questions about the necessity of knowing the mass density for solving the problem.

jsalapide
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1.A 2-meter long wire vibrates with a frequency of 330 Hz when the tension is 500 N. What is the new frequency if the tension on the wire is doubled?

i have no idea how to solve this,, help..
 
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i used the formula f=(n/2L)sqrt(T/mass density)
where n is the number of wave segments formed...

but how would i get the mass density?
 
but how would i get the mass density?
Does it matter? It's the same wire, so surely all you need is the ratio of the root of the two T's in each case? The rest of the variables, except for frequency, are constant.

f_1/f_2 = sqrt{(T_1)/T_2)}
 
If the length and mass density remains the same, the frequency is proportional to square root of the tension.
 

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