Why is s wave shadow zone larger than the p wave shadow zone?

In simple terms the shadow zone of the S-wave is larger because of the Earth's liquid outer core. The S-wave cannot travel through the liquid outer core but the P-waves get refracted at the boundary between the mantle and the outer core. This is why the S-wave shadow zone is larger than the P wave shadow zone.

P waves are refracted at the liquid outer core of the Earth, while S waves are attenuated or stopped entirely. This allows P waves to go "around" the core and reach locations on the far side of the Earth that are within the shadow of the S waves.

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A P-wave is a longitudinal wave with an alternating stretching and compressing motion in the direction of propagation. An S wave is a transverse wave with a vertical motion perpendicular to the direction of propagation.

The shadow zone of a P-wave exists from 105 to 143 degrees (epicentral distance). This is caused by P waves meeting the liquid outer core and being refracted. Part of the P wave is also reflected by the outer core and as a result of the two, a shadow zone exists.

The shadow zone of an S-wave exists from 105 to 180 degrees (epicentral distance). S-waves cannot travel through liquids at all so rather than being refracted by the liquid outer core and traveling through it, they are totally reflected, resulting in a shadow zone from 105 to 180 degrees.