Question

equation of stationary wave

Answer 1

Let us consider a progressive wave of amplitude a and wavelength λ travelling in the direction of X axis.

y1 = a sin 2π [t/T – x/λ] …... (1)

This wave is reflected from a free end and it travels in the negative direction of X axis, then

y2 = a sin 2π [t/T + x/λ] …... (2)

According to principle of superposition, the resultant displacement is,

y = y1+y2

= a [sin 2π (t/T – x/λ) + sin 2π (t/T + x/λ)]

= a [2sin (2πt/T) cos (2πx/λ)]

So, y = 2a cos (2πx/λ) sin (2πt/T) …... (3)

This is the equation of a stationary wave.

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