Confused about scope of accidentals

[smcroberts]

It seems most people here are practicing the classics, but thus far, with rare exceptions, I can only handle simplified classics and pop-tunes. So, I hope my question, though probably stupid, is not too far afield (since I assume that the rules for reading music should be the same across all styles.)

As I understand it, the rule states that an accidental holds sway for a measure over the same note across all octaves. But in the piece I'm working on (Lara's Theme) it seems like the rule should be broken because the bass part has a recurring pattern for several previous measures with f natural, so I wonder if I should really play f-sharp in the bass after the f-sharp in the treble.
Please see the circled notes in the image: are these notes meant to be played as f natural (as indicated in the bass staff's first f in each measure) or f sharp (as indicated in the treble staff's last f)?

Thanks in advance for helping a confused newbie!

[larapool]

I do believe the staves stand alone when it comes to this issue, therefore it would remain a natural.

[Bob]

I don't think it's for all octaves.  Just that one space or line.  Although sometimes publishers/composer write in different styles.

I think that would solve your question.  It's all Bb in the bass. The f# is just a passing or neighbor note in the melody -- not that important.  It's only going to clash for an instant, if you hear it. 

I haven't actually tried that at the piano or with my amazing inner ear, but if you change that f to an f#, you're going to make an augmented chord or it's going to sound like the f# should go up to a g. 

[autodidact]

Accidentals indeed are supposed to apply only to the octave in which they are written, for the duration of the measure.

I always wonder, though, why I so often see naturals written unnecessarily in one measure when the last sharp or flat on that pitch was in the previous measure....

[smcroberts]

Thanks, everyone!

[larapool]

Accidentals indeed are supposed to apply only to the octave in which they are written, for the duration of the measure.

I always wonder, though, why I so often see naturals written unnecessarily in one measure when the last sharp or flat on that pitch was in the previous measure....

The last half of your post was one of the first things I asked my old instructor.  What he told me was that they're basically courtesy accidentals to remind you of the key signature as you play the piece, in case you accidentally keep playing the accidental from the previous measure.