Question

assuming that the frequency 'f' of the guitar made depends on i) applied force ii) mass per unit length. determine the equation of frequency​

Answer 1

Answer:

dimension of frequency=[T

−1

]

Dimension of applied force,F=[MLT

−2

]

dimension of length,l=[L]

dimension of mass per unit length,m=[ML

−1

]

Now suppose,frequency =F^x L^y m^z

so,[T

−1

]= [MLT

−2

]^×[L]^y [ML

−1

]^z

[T

−1

]=[M]^(X+Z)[L]^(X+Y-Z)[T]^(-2X)

Compare both sides,

X+Z=0

X+Y-Z=0

-2X=-1 ⇒X=1/2

So,Z=-1/2 and Y=-1

Hence, frequency is directly proportional to 1/l

(F/m)

Answer 2

Answer:

$f = \frac{1}{2l} \sqrt{\frac{T}{\mu} }$

Explanation:

Frequency = f

Tension or applied force on string = T

mass per unit length = μ

L = length of the string(it is attached at both the ends as they are gitar strings)

Hope it helps

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