What should one do if one is praying behind an imam and one misses one
of the obligatory parts (arkaan)of the prayer?

If someone is praying in a congregation and the loud speaker stops working or the
person is drowsy, and he lags behind the Imam by one or more obligatory acts
(arkaan) of prayer (i.e., the Imam performed it and he could not because of not hearing
the Imam’s voice), then when he returns to consciousness or the sound of the speaker
returns back, he should complete the missed obligatory acts and then continue with the
Imam. This situation has many cases. Take for example the following case: the Imam
recited a verse that contains the word of prostration (sajdah) and the people
misunderstood it to be an actual verse of prostration while in reality it is not, so when
the Imam says takbeer for ruku‘ at the end of the verse and performs ruku‘, some of
the followers (especially those towards the rear of the rows) take it to be the takbeer for
the prostration of recital, thus going into prostration. When the Imam stands up from
the ruku‘ saying “sami‘a Allahu li man hamidah”, they return back (stand up) from
their prostration. Thus, they missed the act of ruku‘ and standing up from it. So it is
incumbent on them to complete what they missed and then catch up with the Imam.
This is because they did not do it intentionally. However, for the one who intentionally
lags behind the Imam (e.g., someone who prolongs his prostration to make a long
supplication such that he misses the obligatory act which is after the prostration) the
majority of the scholars say that the prayer of someone who misses two consecutive
obligatory acts of prayer without a valid excuse, is void and he is sinful.1 However, in
principle the Imam must be followed as said by the Prophet
(peace be upon
him):

The Imam is selected to be followed; the, do not differ with him. When he makes
the takbeer, make the takbeer, when he goes into ruku‘, make ruku‘. When he
says “samia‘ Allahu li man hamidah” (Allah hears he who praises Him), say
“Rabbanaa lakal Hamd” (O our Lord! To You belongs the Praise). When he
goes into sajdah, make sajdah. If he prays sitting, then all should be sitting.

  (Sahih Al-Bukhari, No. 689)