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Yes. This coin is called a Walking Liberty Half Dollar.
the liberty bell in front of the moon
The woman is Miss Liberty! The coins are often called "Morgan" dollars after the man who designed them. Please see the Related Question.
A picture of Miss Liberty on the front and an American Eagle on the back. The same themes were used on all silver dollars up to 1935, just different designs over time.
Chief Engraver Charles E Barber designed a Liberty Head series for dimes, quarters, and half dollars, 1892-1916. Miss Liberty was on one side. The other side of the dime had a wreath, that of the quarter and of the half-dollar an eagle.