Organ Pipes: Wave Reflection Explained

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Sound waves in an open tube reflect due to boundary conditions at the ends of the tube. In an open pipe, the pressure wave must equal zero at the open end, leading to a standing wave described by the sine function. Conversely, in a closed pipe, the pressure gradient is zero at the closed end, resulting in a standing wave described by the cosine function. These conditions create specific wave patterns that facilitate reflection, even in the absence of a physical reflecting medium. Understanding these principles is essential for analyzing sound wave behavior in different types of tubes.
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I want to know that what exactly causes the wave to get reflected in an open tube when there is nothing sort of a reflecting medium.
 
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The sound wave is really a pressure wave, with standing waves of the form
p=cos kx or sin kx. The boundary condition at the x=0 end of an open pipe is that p=0,
giving sin kx. At the x=0 end of a closed pipe, the BC is dp/dx=0 (or p is a maximum),
gilving cos kx.
 
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