Theory of Existence:

PAST PAPERS - 2007

1) State Fourier’s Theorem. What are its limitations?

Answer: Statement: any periodic function of however complex wavelength l can be regarded as made up of definite amplitude, phase and periods, the wavelength of the components being in the ratio l : : :… or the frequencies in the ratio n : 2n : 3n …..

Fourier’s theorem can be expressed by mathematically as:

Y = f(wt) = a = a_o + a₁cos(wt + E₁) + a₂cos(2wt + E₂) + a₃cos(3wt + E₃) +…………..+ a_rcos(rwt + E_r) (1)

OR can be written as

Y = (2)

Where a₁ , a₂,…….. are the amplitudes and E₁, E₂,….. are the initial phases of the components

Its often convenient to express the displacement ‘Y’ as sum of the sine and cosine functions. This can be done by expanding the cosine term in (2)

2) Analyses square wave with the help of Fourier Theorem

3) Obtain an expression for the frequency of transverse vibrations of stretched string. What are its harmonics?

4) Describe Kundt’s tube method to find the velocity of sound in solids