Both parts please. Particularly the end of part c)? How do you know the directio

Question

Both parts please. Particularly the end of part c)? How do you know the direction of travel and what would the expression for the opposite direction be?
b) With the aid of a diagram, describe qualitatively the two normal modes of two identical light pendula coupled by a light spring. Which mode has the highes irequency? 5 narks c) Show that the following expression for the amplitude y(x, t) of a plane wave (z-vol. y(r, t) = Asin is equivalent to the expression x,t)Asin(kr-wt) wiere A desotes the wave amplitude, u is the velocity, A is the wavelength, is 2the angular frequency and k is the wavenumber. In which divection is this wave travelling? Give an expression for a wave travelling in the opposite direct.ion ? ! 5 marks

Explanation / Answer

When the coefficient of x and t are of opposite sign, then wave is traveling in positive x-direction.

When the coefficient of x and t are of same sign, then wave is traveling in negative x direction.

This is the convention followed.

So, for the given eqn, the wave is travelling in +x direction.

For a wave traveling in –x direction, the equation will be:

y = A sin(kx+wt)

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