Question

Assuming that frequency (v) of vibrating string depend up the load (f) applied length of the string (l) and mass per unit length (m) prove that v=1/2l√f/m

Answer 1

Hi my frnd

Take this answer bro!!!

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)

​

This is crrect✓✓✓

Thnx and bye