However, the wave is phase-shifted by φ/2 relative to wave 1. The argument of the sine term in equation (14.22) indicates that we still have a wave with the same frequency and wavelength. The resultant wave is obtained by superposing the two waves. Note that the phase constant φ specifies the extent to which the second wave is shifted along the x – axis relative to the first wave. Interference: Adding waves that differ in Phase onlyĬonsider two waves travelling on the same string with the same amplitude, wavelength and frequency but with a constant phase difference as described by the following equations: The waves may have opposite directions, different amplitudes A, different wavelengths, different frequencies or one wave may differ in phase from the other. When we look at the wave function of either of the two waves y = A sin(kx ± ωt + φ), it is obvious that there are many ways that the two waves can differ. Let us begin with two waves both travelling on the same string. The string shape is found by adding the displacements of the two pulses at every point. As the waves pass each other, the string has a complex shape but the one point on the dashed line is always at rest. (14.10).įig.(14.10) Two wave pulses that are inverted mirror images of each other are produced at the ends of a string. It means that the wave do not alter one another and each propagates through the medium as if the other were not there. This property is called the principle of superposition. When the amplitude of two waves travelling through the same elastic medium is small then, the instantaneous displacement of each particle of the medium is the vector sum of the displacements due to each wave.
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