The highest frequency component of a speech signal needed for telephonic communications is about 3.1 kHz. What is the suitable value for the sampling rate ?

Nyquist Sampling Theorem: 

A continuous-time signal can be represented in its samples and can be recovered back when sampling frequency fs is greater than or equal to twice the highest frequency component of the message signal, i.e.

fs ≥ 2fm

Therefore when we want to convert continuous signals to discrete signals, the sampling must be done at the Nyquist rate.

Calculation:

Given that,

f_m = 3.1 kHz 

⇒ fs ≥ 2f_m

⇒ f_s ≥ 2 × 3.1 = 6.4 kHz