1. Problem from yesterday. What are the answers? What is the decibel level of the lowest “hearable” noise? What is the decibel level of the threshold of pain?

2. More on Intensity Remember the Units for I –Watts / Meter 2 –What is “Watts” a measure of? –What is “Meter 2 ” a measure of?

3. A sound source is doing work on the air. It’s generating power. That power spreads outward in a sphere, spread out on it’s surface.

4. Sound waves carry energy. Energy per second is the power of the wave. The sound intensity is defined as the power that passes through a surface divided by the area of that surface.

5. area of sphere

6. Problem A person stands 3 meters away from a speaker generating 45 watts of power. –What is the intensity heard by the person?

7. Problem A person stands 3 meters away from a speaker generating 45 watts of power. –What is the intensity heard by the person? –What is the dB level?

8. Problem A person stands 3 meters away from a speaker generating 45 watts of power. –What is the farthest a person can stand from this speaker and still hear it?

9. Diffraction Question – –Light and sound are both waves. –If I shine a flashlight out the door, the light goes in a straight line. –If I shout out the door, the sound waves will curve both direction down the hall. Why is this?

10. Diffraction If a wave (any wave) passes through a gap, it will spread out as if the gap were a point source of the wave.

11. Diffraction Works best when the gap matches the wavelength of the wave. Tapers off if the gap gets significantly wider than the wavelength.

12. Diffraction Back to the question – –Light – ~ nanometers –Sound - ~ meters Which will diffract most effectively through a doorway?

13. Phase What is the difference between these two waves?

14. Phase Same amplitude. Same wavelength. The only difference is the phase.

15. Phase Phase is the fraction of the wave cycle that has elapsed.

16. Phase What are some units for “fraction of a cycle?”

17. Phase What are some units for “fraction of a cycle?” Radians, Degrees, and Revolutions.

18. Phase difference Often times, we will want to compare the difference in phase of two waves to see how they will combine.

19. Phase difference. Two waves completely in phase. Crests Line up. Phase difference = 0 Two waves completely out of phase. Crest lines up with trough. Phase difference = 180˚, or ∏ rads, or 1/2 revolution.

20. Phase difference If two waves with different phases interfere, the amplitude of the combined wave will be between the sum of the original two and the difference of the original two.

21. Interference of sound waves The phase of a wave as it reaches a point depends on the distance from that point to the source.

22. Interference of sound waves The phase of a wave as it reaches a point depends on the distance from that point to the source. The phase difference between sound from two sources depends on the path difference between those two sources.

23. Interference of Sound Waves Constructive interference occurs when compressions from both sources hit simultaneously. –Or the two sources are in phase at that point. Path difference between two waves’ motion is some integer multiple of wavelengths Path difference = nλ (n= 0, 1, 2, 3 etc…) Destructive interference occurs when compression lines up rarefaction. –Or the two sources are out of phase at that point. Path difference between two waves’ motion is an odd half wavelength Path difference = (n + ½)λ

24. What does this look like? Two sources –Red is compression –Blue is rarefaction –Light blue lines are nodes where sound level is 0 or quiet. (Destructive Interference). They get equal and opposite compressions and rarefactions. They are “dead zones” and never hear either source.

25. Beats Two waves, with slightly different frequencies, interfere. What will this sound like?

26. Beats

27. Beats are alternations in loudness, due to interference Alternates between constructive and destructive interference. The beat frequency equals the difference in frequency between the two sources: