Answers to Decibel Problems 14–16

14. Use Eq. 2 to calculate the intensity ratio corresponding to each of the following decibel differences: a) 1, b) 2, c) 3, d) 4, e) 5, f) 6.

Answers: (a) 1.26, (b) 1.58, (c) 2.00, (d) 2.51, (e) 3.16, (f) 3.98.


15. Use Eq. 3 to calculate the decibel difference corresponding to the following intensity ratios: a) 2, b) 4, c) 5, d) 8, e) 8 × 103.

Answers: (a) 3.01 dB, (b) 6.02 dB, (c) 6.99 dB, (d) 9.03 dB, (e) 39.0 dB.


16. Use Eq. 3 to calculate the decibel levels in Table 4. Then check the estimated values for accuracy.

Intensity Ratio Decibel Difference
(Estimated)
Decibel Difference
(Calculated)
Percentage Error
1 00.0000
1.25 10.9693.2
1.5 21.7613.6
2 33.010.3
3 54.774.8
4 66.020.3
5 76.990.1
6 87.782.8
7 8.58.450.6
8 99.030.3
9 9.59.540.4
10 1010.00

With the exception of the estimated decibel difference for an intensity ratio of 1.5, the above estimations were fairly accurate.



2013 Robert Chuckrow

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