'berate' vs 'reprimand'
If you berate someone, you speak to them angrily about something they have done wrong. (formal)
⇒ [v n + for] Marion berated Joe for the noise he made. [Also v n]

If someone is reprimanded, they are spoken to angrily or seriously for doing something wrong, usually by a person in authority. (formal)
⇒ [bev-ed + for] He was reprimanded by a teacher for talking in the corridor.

http://www.collinsdictionary.com/dictionary/english-cobuild-learners

Given the definition, they are almost the same meaning. So can these following sentences be interchangeable with the above sentences respectively?

Joe was reprimanded by Marion for the noise he made.
A teacher berated him for talking in the corridor.

Question

'berate' vs 'reprimand'
If you berate someone, you speak to them angrily about something they have done wrong. (formal)   
⇒ [v n + for] Marion berated Joe for the noise he made. [Also v n]

If someone is reprimanded, they are spoken to angrily or seriously for doing something wrong, usually by a person in authority. (formal)   
⇒ [bev-ed + for] He was reprimanded by a teacher for talking in the corridor.

http://www.collinsdictionary.com/dictionary/english-cobuild-learners

Given the definition, they are almost the same meaning. So can these following sentences be interchangeable with the above sentences respectively?

Joe was reprimanded by Marion for the noise he made.
A teacher berated him for talking in the corridor.

Answer

Can I just add something to Brad's excellent explanation?

Neither word is actually used much in everyday modern English. As Brad says, 'reprimand' may be used sometimes in a business context. 'Berate' is hardly used at all.  I don't think I have ever used the word 'reprimand' in my life, and I'm sure that I've never said 'berate'.

The term in common usage, at least in British English, is the phrasal verb 'to tell someone off' or 'to give someone a telling off'.

Answer

"Berate" is more emotional and angry—it is used to show that the person is yelling or being very hard on the person who made the mistake.  "Reprimand" is more official, and may not be emotional at all.  So, for example, an employee who comes to work late will be reprimanded, not berated (at least, not in a professional company!).  However, a frustrated parent may berate a child for spilling milk on the sofa.