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.​

Answer 1

$\huge \underline \mathrm{answer}$

The equation of a travelling wave propagating along the positivey-direction is given by the displacement equation:  ...(i) Linear mass density, Frequency of the tuning fork, Amplitude of the wave,   ...(ii) Mass of the pan, m   Tension in the string, The velocity of the transverse wave v, is given by the relation:     Angular Frequency,                                                                              ...(iii) Wavelength, Propagation constant,                                                ...(iv) Substituting the values from equations (ii), (iii), and (iv) in equation (i), we get the displacement equation: .

Answer 2

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