This image does not actually show a plane flying dangerously low over a crowded beach in California, according to collector Alan Mays; note that there is no reflection of the biplane in the water at all.
Mays wrote on his Flickr page that the two men were most likely photographed while sitting in a stationary airplane, then that negative was developed on top of a second photograph:
Fortunately, the two aeronautical gents pictured here in this souvenir real photo postcard are safely ensconced in a photographer's studio and aren't actually risking catastrophe by flying low over the heads of oblivious beachgoers. The "Los Angeles" and "California" pennants hanging on the plane presumably identify the location.
Although we have not been able to pinpoint exactly when this image was created or identify the two men in the plane (Mays said the postcard is dated 1911), we were able to track down the original picture of people on the beach, which was taken in Long Beach, California by C.C. Pierce. The Huntington Library, where the image is archived, did not provide a date for the photograph, but Pierce lived between 1861 and 1946, and established his own studio in 1900.
For comparison's sake, here is the souvenir postcard compared to Pierce's original image:
It was very common in the past to physically manipulate photographs to make joke or hoax images (some of which made their way onto postcards), much as manipulated images are sometimes used online today.