About you question: the most common approach I have seen, is to have one activity diagram per use case.
A few points about your use case diagram:
1- I have never seen multiple specialization in use case diagrams. you may want to reconsider that. When use case A (child) specializes use case B (parent) it inherits all the preconditions, post-conditions, main flow and alternative flow steps. I can guess that this features are not the same for your parent use cases (for example turn volume up and turn on); therefore multiple specialization does not makes sense here, to say the least.
2- Use case generalization should be avoided unless it adds real value to your model. It is not very intuitive and makes your diagrams vague.
3- This use case diagram seems to have the tendency to view use cases as classes and generalization as inheritance; which is not correct.
4- You may want to reconsider the level of granularity of your use cases as well; turn on with IR/Knob and turn off with IR/Knob may all be integrated in one reasonable sized use case with some alternative flows. But this is a choice you make as a requirements engineer, anyone may do it differently.
I recommend you take a look at section 5.3 of UML 2 and the Unified Process book which is about use case generalization.
Suggestion:
Let's assume you want to keep separate use cases for turning on and off and focus on one use case (turning on):
1- If the steps for turning on with IR are totally different from turning on with knob, make the turn on use case abstract and do not write any spec (text) or draw any activity diagram for it. Then specialize two use cases called turn on with knob and turn on with IR which are concrete with separate specs and/or activity diagrams.
2- If the steps for turning on with IR are almost the same as turning on with knob except for one step where the user chooses IR or Knob; you could use alternative flows. In this case you can have only one use case with one spec and/or one activity diagram.
Do the same for other three use cases.