Question

Question-
A slab whose dielectric constant is K, is attached to a string of linear mass density u, while its one end is fixed to a rigid support. Its cross section has sqaure plates of side b and seperation between them is d. Find the fundamental frequency of the vibration of the string.

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Answer 1

$\huge \fbox{ \underline \purple{Answer }}$

Let us write the given data and solve the question

Density = U

Cross section of plates = b

Separation = d

Fundamental frequency (n) = ?

SOLUTION:

Let us use that formula here

n = 1/2L  √T/μ

As we already know the value of T from the given data

Let us try to derive the value of T

T =  -dU/dx  =  1/2(k-1)E₀ bV²/ d      equation 1

Let us apply the value of T in frequency formula (n)

Then,

n =   1/2L √(k-1)E₀bV² /2dμ

This is final equation or Fundamental Frequency which we require

If it is confusing please refer the given attachment

Sorry for the inconvenience

Hope it helps

Thanks for asking

Stay blessed and safe

Answer 2

Answer:

Let us write the given data and solve the question

Density = U

Cross section of plates = b

Separation = d

Fundamental frequency (n) = ?

SOLUTION:

Let us use that formula here

n = 1/2L  √T/μ

As we already know the value of T from the given data

Let us try to derive the value of T

T =  -dU/dx  =  1/2(k-1)E₀ bV²/ d      equation 1

Let us apply the value of T in frequency formula (n)

Then,

n =   1/2L √(k-1)E₀bV² /2dμ

This is final equation or Fundamental Frequency which we require

If it is confusing please refer the given attachment

Sorry for the inconvenience

Hope it helps

Thanks for asking

Stay blessed and safe