RSI settings depend on your analysis objectives. The default setting for RSI is 14 periods. However, when looking for short-term overbought/oversold readings, I like to use a shorter look-back period. Often, this is 10 days, which covers two weeks. When looking to capture general trend, a longer look-back period works better because it is less choppy.
The sensitivity of a momentum oscillator depends on the number of look-back periods. 10-period RSI will be more sensitive than 20-period RSI. This means 10-period RSI will produce more overbought (>70) and oversold readings (<30). 10-period RSI will also cross above/below 50 more often than 20-period RSI. Conversely, 20-period RSI will cross above/below 50 fewer times. This makes the longer version better suited for overall trend identification. Momentum favors an uptrend when RSI is above 50 and a downtrend when below 50.
The chart above shows RSI with 10, 14 and 20 periods. Notice that the actual line shapes are virtually equal. The biggest difference is the number of overbought/oversold readings and the crosses above/below 50.
Oscillator sensitivity is also influenced by the underlying security. Volatile securities will produce wider swings in RSI. An index, like the S&P 500, is generally less volatile than individual stocks. 10-period RSI for Amazon will be more volatile than 10-period RSI for the S&P 500. You can learn more about RSI in the Chart School.