Could someone describe what happens to the relative humidity of moist air as the air travels over the Cascades

Relative humidity is the percentage of the actual water vapor content compared with the saturation vapor pressure. Saturated air has a relative humidity of 100 percent, whereas totally dry air (which never occurs in the atmosphere) would have a relative humidity of 0 percent.

here is an example:
When air moves up and over a mountain or ridge, in a process called orographic lifting, it cools as it rises. (As the pressure decreases, the air "expands," and the air molecules move more slowly). If the rising air cools enough, its temperature will reach the dew point, the temperature at which air is saturated. At that temperature, condensation will begin; this is the point at which water vapor begins to be converted to liquid water, the result being clouds and precipitation.

Because a steep mountainside can force air upward very quickly over a short distance, orographic lift can produce heavy rain or snow along the side of the mountain range that faces the wind, if enough moisture is present in the air. In the western United States, some mountain ranges are aligned north-to-south, with their western slopes facing the Pacific Ocean and its abundant moisture. Ski resorts in the Cascade Range of Washington and Oregon, and the Lake Tahoe region in the Sierra Nevada, for example, benefit from orographically produced snowfall.

When the air rises to and passes over a mountain or ridge, it begins to descend down the other side. Descending air warms, and as it does, the saturation vapor pressure increases. But because no water is being added to the air, the actual vapor pressure stays the same. Thus the relative humidity becomes lower, and the air gets drier. This process causes the lee side of the mountains (i.e., the side away from the prevailing winds) to be a zone of limited precipitation known as a rain shadow. Rain shadows are major contributors to the climate of certain parts of the world. In the example above, the regions east of the Cascades in Oregon and Washington, and east of the Sierra Nevada Mountains in California, are arid as a result of the rain shadow effect.