I read in my physics book that when we use a spoon and vibrate a glass, the pitch should be according to the air column inside. So, less filled the glass, longer the air column and lesser the frequency according to frequency = 1/4*( v/l) formula. But when I tried to do it practically I found the glass which has the least amount of water sounds shriller meaning high frequency. Why so? Am I doing something wrong in my exp? Here is a link where this person does the same experiment but she does not explain the physics
I read in my physics book that when we use a spoon and vibrate a glass, the pitch should be according to the air column inside.
The book is wrong. The pitch depends on the vibration of the glass, not the air inside.
The glass changes shape as it vibrates, and when you add water, the water also has to move to match the shape of the glass. The extra mass of the water lowers the vibration frequency.
If you want to make the air inside a container vibrate, get a bottle with a fairly narrow neck and blow across the neck of the bottle. With a bit of practice you will be able to produce a tone. If you then partly fill the bottle with water, the vibrating air column will be shorter and the pitch will be higher.