We may learn (how) to play a musical instrument. When we learn to play an instrument, we acquire the skills to play a type of instrument.
He learned (how) to play the piano.
We may learn to play an instrument using a particular instrument of its type. We use the preposition on to refer to the particular instrument being played; it is the vehicle or platform on which the learning takes place:
He learned to play the piano on an old upright acquired from
a speakeasy that was very popular during the Prohibition Era.
This is the piano he learned to play on.
P.S. Consider these sentences without on:
This is the piano he played.
This is the piano he learned to play.odd
The first sentence refers to a specific piano. It is easy to think of a real-world scenario where one might refer to the specific instrument:
This is the very piano he played in his Carnegie Hall debut. Bids will start at $250,000.
But if we refer to the specific instrument with learn, the listener may infer that there is something atypical about that piano which itself had to be learned, that the piano was in some way not representative of its type. That is not usually the case, but it is not impossible. Therefore, we cannot say that on is compulsory. But in most cases, the instrument is going to be representative of its type, and there will be nothing atypical about it, and if we don't want the listener to think there was something atypical, we would say:
This is the piano he learned on.
In general, some adjectives go with certain prepositions, but some adjectives can go with more than one preposition (and context will determine which preposition fits better, though in many cases the use of one preposition doesn't rule out other prepositions, as the meaning doesn't really change). With "surprised," I think it's safe to say that "by" and "at" are more common, but you'll also find "about" and "with." There is no fixed pattern; the more you read, the easier it becomes knowing which preposition to use (or not use).
Best Answer
Traditionally, by indicated an agent, the doer of the action, and with indicated the instrument used by the agent.
However, there's a large grey area between the two.
If a fan hit Andrew with a stone, the implication is that the fan was holding the stone and using it as a weapon.
If Andrew was hit by a stone, the implication is that the fan threw the stone at Andrew or, in other circumstances, that the stone was dislodged and fell on Andrew.
The same applies to plastic bottles. One can be struck with a plastic bottle or by a plastic bottle.
When it comes to missiles, it's more complicated. People are struck by bullets and arrows, even though these are instruments rather than agents. You can also be struck by a (flying) knife although you are more likely to be stabbed with one.
We also talk about people being hit by a bus and killed by falling trees. You might be killed with a tree, but only if somebody was using the tree to kill you, which is a bit improbable although not impossible.
So the choice of preposition depends on the context and on idiomatic use.
http://www.grammaring.com/the-agent-with-the-passive-voice https://teddymedinal.blogspot.com/2015/01/prepositions-of-agent-or-instrument.html