Question

frequency of a sonometer wire depends upon the linear mass density of the wire and tension in the wire (T) and acceleration due to gravity (g). derive the relation of frequency using dimensional analysis​

Answer 1

Explanation:

11th

Physics

Units and Measurement

Dimensions and Dimensional Analysis

The frequency (f) of a stre...

PHYSICS

The frequency (f) of a stretched string depends upon the tension F (dimensions of force), length l of the string and the mass per unit length μ of string. Derive the formula for frequency.

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ANSWER

Suppose, that the frequency f depends on the tension raised to the power a, length raised to the power b and mass per unit length raised to the power c. 

Then, f∝[F]a[l]b[μ]c

or, f=k[F]a[l]b[μ]c ...(i)

Here, k is a dimensionless constant. 

Thus, [f]=[F]a[l]b[μ]c

or, [M0L0T−1]=[MLT−2]e[L]b[ML−1]c

or, [M0L0T−1]=[Ma+cLa+b−cT−2a]

For dimensional balance, the dimensions on both sides should be same.

Thus, a+c=0 ...(ii)

a+b−c=0 ...(iii)

−2a=−1 ...(iv)

Solving these three equations, we get

a=21,c=−21