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

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Doubling the tension in a vibrating wire affects its frequency according to the relationship between tension and frequency. The formula f = (n/2L)√(T/mass density) indicates that frequency is proportional to the square root of tension when length and mass density remain constant. Therefore, if the tension is increased from 500 N to 1000 N, the new frequency can be calculated using the ratio of the square roots of the tensions. The discussion emphasizes that the mass density remains unchanged, simplifying the calculation. Understanding this relationship allows for predicting changes in frequency based on tension adjustments.
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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