having equal and opposite displacements moving in opposite directions. The overlapping pulses add up to zero displacement in curve (c). y = f ( x–vt ) , y = f ( x–vt ), .......... ..........
y n = f n ( x–vt ) then the wave function describing the disturbance in the medium is y = f ( x – vt ) + f ( x – vt ) + ...+ f n ( x – vt ) = i n f x vt i ∑ ( . ) The principle of superposition is basic to the phenomenon of interference. For simplicity, consider two harmonic travelling waves on a stretched string, both with the same ω (angular frequency) and k (wave number), and, therefore, the same wavelength λ . Their wave speed will be identical.
Let us further assume that their amplitudes are equal and they are both travelling in the positive direction of x -axis. The waves only differ in their initial phase. According to Eq. ( .
), the two waves are described by the functions: y ( x, t) = a sin ( kx – ω t ) ( . ) and y ( x, t) = a sin ( kx – ω t + φ ) ( . ) The net displacement is then, by the principle of superposition, given by y ( x, t ) = a sin ( kx – ω t ) + a sin ( kx – ω t + φ ) ( . )