1. Speed of sound

2. Problem During a thunderstorm, lightning strikes 300 m away. If the air temp is 25 Celsius, how much time passes between when you see the lightning and hear the thunder?

3. Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency Motion together = higher frequency. Motion away = lower frequency. All waves do this. Including light.

4. For a stationary source, a compression reaches the observer once a period. If the source moves, each compression has less distance to travel, so it takes less time to get there, so the frequency is higher to the observer. Moving Source.

5. Moving Source Behind the truck the opposite happens. Each wave starts out from farther away, has more distance to travel, takes more time. So, the observed frequency is lower.

6. Doppler Effect, (Observer Toward Source) An observer is moving toward a stationary source. Due to his movement, the observer crosses crests more often. The frequency heard is increased

7. Doppler Effect, Case 1 (Observer Away from Source) An observer is moving away from a stationary source The observer crosses fewer crests per second The frequency appears lower

8. Equation for the doppler effect f o = observed frequency f s = source frequency v = speed of sound v o = observer velocity v s = source velocity v o – positive if moving towards each other v s – positive if moving away from each other

9. A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at the crossing, when the train is (a) approaching and (b) leaving the crossing? A problem.

10. Question What happens to this equation when the object is moving towards you at the speed of sound?

11. Shock Waves A shock wave results when the source velocity exceeds the speed of the wave itself The circles represent the wave fronts emitted by the source

12. Shock waves. The wave front is the edge of the cone made up of the circles.

13. Shock Waves, cont Mach number – velocity /speed of sound

14. Shock Waves, cont Mach number – velocity /speed of sound Also, sin θ = 1/Mach Number

15. Shock Waves, final Sonic Boom Video http://www.youtube.com/watch?v=- d9A2oq1N38&feature=related http://en.wikipedia.org/wiki/Chuck_Yeager http://en.wikipedia.org/wiki/File:Bell_X-1_color.jpg http://space.about.com/b/2004/02/20/john-glenn-first- american-to-orbit-earth.htm

16. Transition: New Subject

17. New Symbol “I” – Intensity One description of the loudness of a noise. Measured in Watts/meter 2

18. Sound Intensities Threshold of hearing (I 0 ) Faintest sound most humans can hear Add to WOD: Faintest: 1 x 10 -12 W/m 2 Threshold of pain Loudest sound most humans can tolerate Add to WOD: Loudest (Tolerate): About 1 W/m 2

19. New Symbol Decibels (dB) “β“ – beta – decibel level of sound. A much more common measure of “loudness” Measured in decibels (dB)

20. Intensity Level of Sound Waves Add above equation to decibel WOD:

21. Remember logarithms? Every number can be rewritten as 10 something. That’s what a log is. 100 = 10 2 so log 100 = 2.1 = 10 -1 so log.1 = -1 32 = 10 1.505 so log 32 = 1.505

22. Log tricks Log 1 = 0. Log (A*B) = Log (A) + Log (B) Log (A/B) = Log (A) – Log(B)

23. Intensity Level of Sound Waves Plug in some values for I If I = I 0, β = 0. Lowest “hearable” sound.

24. Last note on dB scale dB is a logarithmic scale. 10 x as much noise doesn’t multiply dBs by ten. It adds 10 dB to existing level. Double dB is not Double Frequency. 50dB to 100dB is not double sound loudness. 50 to 60 is x10, 60 to 70 is x10, 70 to 80 is x10, 80 to 90 is x10, 90 to 100 is x10. So 50 to 100 is x10x10x10x10x10= x100,000 50 to 100 is x100,000, NOT double.

25. Problem What is the decibel level of the lowest “hearable” noise? What is the decibel level of the threshold of pain?