A plane harmonic pressure wave is propagating in air in $$X-direction$$. There is a rigid fixed infinitely large wall at $$yz-plane$$. The wave gets reflected back by the wall. In this process, the layer of fluid in contact with wall pushes back on the adjacent layer very hard, since it has no where to go. This over – push – back causes the adjacent layer to recoil in the reverse direction, in turn it pushes on its neighbor on the side away from the wall and so on. There is thus a travelling wave that has reverse direction, it has reflected off the wall with no loss of energy. Equation of incident displacement wave is given as $$S=S0sinkx$$−ωt. (B$$ is Bulk modulus of $$air), Then

Question

A plane harmonic pressure wave is propagating in air in $$X-direction$$. There is a rigid fixed infinitely large wall at $$yz-plane$$. The wave gets reflected back by the wall. In this process, the layer of fluid in contact with wall pushes back on the adjacent layer very hard, since it has no where to go. This over – push – back causes the adjacent layer to recoil in the reverse direction, in turn it pushes on its neighbor on the side away from the wall and so on. There is thus a travelling wave that has reverse direction, it has reflected off the wall with no loss of energy. Equation of incident displacement wave is given as  $$S=S0sinkx$$−ωt. (B$$ is Bulk modulus of $$air), Then

Infinity Learn · Accepted Answer

∵$$S=S0sin$$⁡$${$$$$kx$$−ω$$t}P=$$−B∂Sδ$$x=$$−$$BS0kcos$$⁡$${$$$$kx$$−ω$$t}Due$$ to reflection from rigid boundary, compression pulse will get reflected as compression pulse∴$$Pr=$$−$$BS0kcos$$⁡$${$$$$kx$$$$+$$ω$$t}=BS0kcos$$⁡$${$$$$kx$$$$+$$ω$$t+$$π$$}$$∴$$Sr=S0sin$$⁡$${$$−$$kx$$−ω$$t+$$π$$}$$

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