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Chapter 20: Q33P (page 527)

A spectrum has a signal-to-noise ratio of 8/1. How many spectra must be averaged to increase the signal-to-noise ratio to 20 / 1?

Short Answer

Expert verified

The spectra must be averaged to increase the signal-to-noise ratio to 20 / 1 is 7 scans required.

Step by step solution

01

Definition of Signal to noise

  • In science and engineering, the signal-to-noise ratio compares the level of a desired signal to the amount of background noise.
  • The signal-to-noise ratio (SNR) is frequently given in decibels and is defined as the ratio of signal power to noise power.
02

Determine the many spectra must be averaged to increase the signal-to-noise ratio to 20 / 1

  • The spectra must be averaged in order to enhance the signal-to-noise ratio to 20 / 1.
  • Initial ratio is as follows: 8/1
  • The signal-to-noise ratio is increased by averaging the factor of a particular ratio 2.5
  • It must now raise the ratio from 8 to 20 (factor of208=2.5)
  • As a result, the necessary factor is2.52=6.25there are around 7 scans.
  • To boost the signal-to-noise ratio to 20 / 1, the spectra must be averaged, which takes 7 scans.

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Most popular questions from this chapter

The exitance (power per unit area per unit wavelength) from a blackbody (Box 20-1) is given by the Planck distribution: Mλ=2πhc2λ5(1ehc/Akt-1)where λis wavelength, Tis temperature K), his Planck’s constant, Cis the speed of light, and kis Boltzmann’s constant. The area under each curve between two wavelengths in the blackbody graph in Box 20-1is equal to the power per unit area(W/m2)emitted between those two wavelengths. We find the area by integrating the Planck function between wavelengthsλ1andλ2

role="math" localid="1664862982839" Poweremitted=∫λ1λ2Mλdλ

For a narrow wavelength range, ∆λ1the value of Mλis nearly constant and the power emitted is simply the product Mλ∆λ2.

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