Question

The infrared spectrum of a sample was collected by averaging 8 individual scans. The resulting signal-to-noise ratio was determined to be 4:1. How many scans must be averaged to obtain a signal-to-noise ratio of 32:1?

Answer 1

Sol.

(s/n)2 = (s/n)1 × (n2/n1)^1/2

where (s/n)2 and (s/n)1 are final and initial signal to noise ratios respectively

n2 = Final number of individual scans averaged

n1 = Initial number of individual scans averaged

Given that

n1 = 8 , (s/n)1 = 4 , (s/n)2 = 32

Therefore ,

32 = 4 × (n2/8)^1/2

32/4 = (n2/8)^1/2

n2/8 = (8)² = 64

n2 = 64 × 8 = 512

The answer is   512