from Eq. ( . ), given by, v = γ P ( . ) This modification of Newton’s formula is referred to as the Laplace correction .
For air γ = / . Now using Eq. ( . ) to estimate the speed of sound in air at STP, we get a value .
m s – , which agrees with the measured speed. . THE PRINCIPLE OF SUPERPOSITION OF WAVES What happens when two wave pulses travelling in opposite directions cross each other (Fig. .
)? It turns out that wave pulses continue to retain their identities after they have crossed. However, during the time they overlap, the wave pattern is different from either of the pulses. Figure .
shows the situation when two pulses of equal and opposite shapes move towards each other. When the pulses overlap, the resultant displacement is the algebraic sum of the displacement due to each pulse. This is known as the principle of superposition of waves. According to this principle, each pulse moves as if others are not present.
The constituents of the medium, therefore, suffer displacments due to both and since the displacements can be positive and negative, the net displacement is an algebraic sum of the two. Fig. . gives graphs of the wave shape at different times.
Note the dramatic effect in the graph (c); the displacements due to the two pulses have exactly cancelled each other and there is zero displacement throughout. To put the principle of superposition mathematically, let y ( x , t ) and y ( x , t ) be the displacements due to two wave disturbances in the medium. If the waves arrive in a region simultaneously, and therefore, overlap, the net displacement y ( x , t ) is given by y ( x, t ) = y ( x, t ) + y ( x, t ) ( . ) If we have two or more waves moving in the medium the resultant waveform is the sum of wave functions of individual waves.
That is, if the wave functions of the moving waves are Fig. . Two pulses