dimensional analysis

R

RM2020

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Oct 31, 2020
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need this to pass my 1st assignment

A guitar string, made by your Musical Instruments division, has mass (m), length (?) and tension (F). It is proposed by one of your junior colleagues that a formula for the period of vibration (t) of the string might be;
Q1B formula.PNG


Use dimensional analysis to show your colleague that this formula is incorrect

literally over my head in this level of maths ( i work with my hands )
 
[MATH]t[/MATH] is time in seconds

[MATH]2\pi[/MATH] is a unitless constant

[MATH]m[/MATH] is mass in [MATH]kg[/MATH]
[MATH]L[/MATH] is length in meters

force, [MATH]F[/MATH], is measured in Newtons, [MATH]N = \dfrac{kg \cdot meter}{sec^2} [/MATH]
place all the units in the formula and see what you get
 
1604511469781.png

hi
Sorry I'm confused
I had managed to get this far with the equation but stumped
just need to know the outcome of the formula to prove the sum is not correct (i.e T )
 
[MATH]t = 2\pi \sqrt{\dfrac{m^3 L}{F}} = 2\pi \sqrt{\dfrac{m^3 L}{1} \cdot \dfrac{1}{F}} = 2\pi \sqrt{\color{red}\dfrac{kg^3 \cdot meter}{1} \cdot \dfrac{sec^2}{kg \cdot meter}}[/MATH]
dividing out the units and taking the square root, what units do you end up with?
 
sorry
its been 30yrs since i did maths, and ive been having private lessons but you do it a different way to my tutor ( losing the will to live )
 
I recommend you see your tutor for an explanation that you understand.

FYI, the simplified units within the radical become [MATH]\sqrt{kg^2 \cdot sec^2} = kg \cdot sec \ne sec[/MATH]
 
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