S302, Kewley-Port 9/30/07

**Homework 6 **

**Decibels **

1. Given the relative intensity ratios below, fill in the table for the corresponding log and dB values.

Ratio | Log | dB |

1:1 | ||

10:1 | ||

1000:1 | (3) | (30) |

1:10 | ||

5:1 | ||

1:50 |

2. Convert the following decibel values to intensity ratios.

10 dB (10:1)

-10 dB

23 dB

3. Given the absolute intensities below (in watts/m^{2}),
compute the corresponding dB IL values for I_{r} = 10^{-12}w/m^{2}

10^{-6} (60 dB IL)

10^{
-12}

10^{0}

1.25 · 10^{-12}

5 · 10^{-12}

4. Two abolute intensities are equal. What is the dB difference between them?

5. Given the relative pressure ratios below, fill in the table for the corresponding log and dB values.

Ratio | Log | dB |

1:1 | ||

10:1 | ||

1000:1 | (3) | (60) |

1:10 | ||

5:1 | ||

1:50 |

6. Convert the following decibel values to pressure ratios.

20 dB

-40 dB

46 dB

7. Given the absolute pressures below (in Pa),
compute the corresponding dB SPL values for P_{r} = 2
X 10^{1 } Pa.

2 · 10^{2} (20)

2 · 10^{4}

8 · 10^{3}

4.25 · 10^{5}

8. An increase in intensity by a factor of two corresponds to an increase of how many decibels?

9. An decrease in intensity by a factor of two corresponds to a decrease of how many decibels?

10. An increase in sound pressure by a factor of two corresponds to an increase of how many decibels?

11. If one lion roars at 82 dB IL, how loud are ten such lions?

12. There are two fans, one with sound level of 60 dB IL, and the other with sound level of 70 dB IL. What is the sound level when both fans are on at the same time?

13. a) What is the ratio of two pressures if their difference is 0 dB?

b) If a sound was measured as 0 dB IL, what is it intensity?

14. If one correlated pressure is 4 times another, how many dB greater is it?

15. Does 0 dB SPL mean the absence of sound? Explain.

16. The pressures from two uncorrelated sources were measures as 80 dB SPL , and p2 = 83dB SPL.

a) What is the total intensity of the combined sound?

b) What is the resulting sound level in dB SPL?

17. It is most convenient to express time in milliseconds for sounds related to speech. 1000ms = 1 s. For the following F0 values, write one the frequency and period of the first three harmonics:

a) F0 = 125 Hz (average male)

b) F0 = 220 Hz (average female)

c) F0 = 300 Hz (small child)

18. Define aperiodic sounds, and give two examples from speech.