In a 10-bit PCM system, a message signal having maximum frequency of 4 KHz is to be transmitted. If the bit rate of this PCM system is 60 Kbits / sec, the appropriate sampling frequency is

Concept: 

The bandwidth of a PCM system for an encoded signal sampled at a frequency of fs is given by:

Bit rate = n fS

fS = Sampling frequency

n = number of bits used for encoding.

n is related to the number of quantization levels (L) as:

L = 2n

n = log2 L

Calculation:

the maximum frequency for the signal will be 4 kHz.

n = 10 bits, R_b = 60 Kbits/sec

Bit rate = n fS

f_s = 6 kHz

And f_m is given as 4 kHz i.e

f_s ≥ 2f_m

f_s ≥ 8 kHz

So, f_s = 6kHz leads to undersampling.

Hence, option 1 and 2 can't be correct.

Option 4: f_s = 9 kHz leads to oversampling

Hence, option 3 is correct f_s = 8 kHz 

∴ The appropriate value of the sampling frequency (fs) will be 8 kHz