How to join two dataframes for which column values are within a certain range?

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One simple solution is create interval index from start and end setting closed = both then use get_loc to get the event i.e (Hope all the date times are in timestamps dtype ) 

df_2.index = pd.IntervalIndex.from_arrays(df_2['start'],df_2['end'],closed='both')
df_1['event'] = df_1['timestamp'].apply(lambda x : df_2.iloc[df_2.index.get_loc(x)]['event'])

Output : 

            timestamp         A         B event
0 2016-05-14 10:54:33  0.020228  0.026572    E1
1 2016-05-14 10:54:34  0.057780  0.175499    E2
2 2016-05-14 10:54:35  0.098808  0.620986    E2
3 2016-05-14 10:54:36  0.158789  1.014819    E2
4 2016-05-14 10:54:39  0.038129  2.384590    E3

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