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 | 0 | 0.000 | 0 |
| 1.25 | 1 | 0.969 | 3.2 |
| 1.5 | 2 | 1.76 | 13.6 |
| 2 | 3 | 3.01 | 0.3 |
| 3 | 5 | 4.77 | 4.8 |
| 4 | 6 | 6.02 | 0.3 |
| 5 | 7 | 6.99 | 0.1 |
| 6 | 8 | 7.78 | 2.8 |
| 7 | 8.5 | 8.45 | 0.6 |
| 8 | 9 | 9.03 | 0.3 |
| 9 | 9.5 | 9.54 | 0.4 |
| 10 | 10 | 10.0 | 0 |
With the exception of the estimated decibel difference for an intensity ratio of 1.5, the above estimations were fairly accurate.
©2013 Robert Chuckrow