Answers to Decibel Problems 17–23

17. Estimate the intensity level in dB of the threshold of audibility at each of the following frequencies: a) 30 Hz, b) 100 Hz, c) 1,000 Hz, d) 5,000 Hz. To do this problem, use the bottom (broken) curve of the equal-loudness curves. Trace that curve to where it intersects the at each frequency mentioned. Then read off the corresponding dB level on the vertical scale on the left.

Answers: a) 60 dB, b) 25 dB, c) 4 dB, d) –4 dB.


18. Estimate the decibel difference corresponding to each of the following intensity ratios: a) 1.25, b) 2, c) 4, d) 5, e) 8, f) 10, g) 20, h) 100, i) 125, j) 200, k) 1,000, l) 1,000,000.

Answers: a) 1 dB, b) 3 dB, c) 6 dB, d) 7 dB, e) 9 dB, f) 10 dB, g) 13 dB, h) 20 dB, i) 21 dB, j) 23 dB, k) 30 dB, l) 60 dB.


19. Estimate the intensity ratio corresponding to each of the following decibel differences: a) 1 dB, b) 3 dB, c) 6 dB, d) 9 dB, e) 10 dB, f) 11 dB, g) 13 dB, h) 16 dB, i) 30 dB, j) 50 dB, k) 53 dB.

Answers: a) 1.25, b) 2, c) 4, d) 8, e) 10, f) 12.5, g) 20, h) 40, i) 1,000, j) 100,000, k) 200,000.


20. A sound source produces an intensity of 10–9 W/m2 at 10 ft away. Estimate the intensity at each of the following distances from the source: a) 20 ft, b) 30 ft, c) 40 ft, d) 50 ft, e) 100 ft.

Answers: a) (1/4) × 10–9 = 2.5 × 10–10 W/m2, b) (1/9) × 10–9 = 1.11 × 10–10 W/m2, c) (1/16) × 10–9 = 6.25 × 10–11 W/m2, d) (1/25) × 10–9 = 4 × 10–11 W/m2, e) (1/10,000) × 10–9 = 10–13 W/m2.


21. A sound source produces 40 dB at 10 ft away. Estimate the decibel level at each of the following distances from the source: a) 20 ft, b) 30 ft, c) 40 ft, d) 50 ft, e) 100 ft. Answers: a) 34 dB, b) 30 dB, c) 28 dB, d) 26 dB, e) 20 dB.


22. At what decibel level is a 100-Hz sound as loud as a 1,000-Hz sound at 40 dB?

Answer: 51 dB.


23. At what decibel level is a 30-Hz sound as loud as a 3,000-Hz sound at 50 dB?

Answer: 77 dB.



2013 Robert Chuckrow


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