The figure below shows a six$-$string guitar and the distance between the bridge and the fret closest to the bridge.

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$($i$)$

$($a$)$ When the thinnest string is pressed down at the fret closest to the bridpe $(d=20\mathrm{.}5cm)$ and the string plucked near the midpoint, the vibrating string produces a sound with a frequency of $2,380Hz.$ If the guitarist moves to the next fret $($second$-$closest to the bridge$),$ the sound produced has a frequency of $2,242Hz.$ Determine the distance $($in cm $)$ between the frets. $($Assume the given frequencies are fundamental frequencies.$)$

$1\mathrm{.}25$

$q,$

$cm$

$($b$)$ What If$?$ All the guitar strings are made of the same material and the second$-$thinnest string has a diameter that is $22\mathrm{.}2\%$ larger than that of the thinnest string. What is the frequency $($in Hz $)$ of the note played when the second$-$thinnest string is pressed at the fret closest to the bridge?

$q,$

Read the statement of the problem carefully. Is the linear mass density or the diameter of the string larger by $22\mathrm{.}2\%?$ Your answer indicates that you chose the linear mass density rather than the diameter of the string to be $22\mathrm{.}2\%$ larger. Hz

What is the frequency $($in Hz $)$ of the note when the second$-$thinnest string is pressed at the next fret $($second$-$closest to the bridge$)?$

Read the statement of the problem carefully. Is the linear mass density or the diameter of the string larger by $22\mathrm{.}2\%?$ Your answer Indicates that you chose the linear mass density rather than the diameter of the string to be $22\mathrm{.}2\%$ larger. Hz