if the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?

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09-12-2022
Physics

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if the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?

Answer :

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varshamittal029 varshamittal029 · Answer 1 · 2022-12-17T04:21:10-05:00

The correct option is B) [tex]d_{low} = 4d_{high}[/tex].The diameter of the lowest string is four times that of the highest string.

Because frequency is inversely proportional to the square root of mass density, the low string's mass density would be 16 times greater. The radius would increase by 4 times as a result.

If the diameter is same, the mass is same and the speed is 1/4 times due to the square root sign in the denominator. The frequency is 1/4 times because the wavelength is constant.

The relationship between frequency and diameter of a string is given by,

[tex]f=\frac{1}{L*d} \sqrt{\frac{4T}{\rho \pi}}[/tex]

Where,

L = length of the string

d= diameter of the string

T= tension of the string

[tex]\rho[/tex] = density of the string

Given, that the lengths of the strings are same; tension of the strings are same and as the string are of same material then the density of the strings are also same.

Thus, the frequency is inversely proportional to the string diameter.

f = 1/d

So, if

[tex]4f_{low} = f_{high}[/tex]

Then,

[tex]d_{low} = 4d_{high}[/tex]

Thus,the diameter of lowest string is 4 times the diameter of highest string.

To learn more about frequency of string refer here

https://brainly.com/question/13552044

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Your question is incomplete, here is the complete question

The 6 strings on a guitar all have about the same length and are stretched with about the same tension.The highest string vibrates with a frequency that is 4 times that of the lowest string.

If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?

[tex]A.\ d_{low}=2d_{high}\\\\B.\ d_{low}=4d_{high}\\\\C.\ d_{low}=16d_{high}[/tex]