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PHYSICS 231 INTRODUCTORY PHYSICS I

This lecture covers the speed of sound in fluids, intensity and intensity level, spherical waves, Doppler effect, shock waves, standing waves, and interference of sound waves. Includes examples and applications.

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PHYSICS 231 INTRODUCTORY PHYSICS I

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  1. PHYSICS 231INTRODUCTORY PHYSICS I Lecture 23

  2. Last Lecture -Sound • Speed of sound in fluid (for solid, replace ) • Intensity • Intensity Level - dB • Spherical Waves

  3. Doppler Effect, Moving Observer Towards source: Away from source: v = speed of sound, vO = speed of observer

  4. Doppler Effect:Source in Motion

  5. Doppler Effect, Source in Motion Approaching source: Source leaving:

  6. Example 14.6 An train has a brass band playing a song on a flatcar. As the train approaches the station at 21.4 m/s, a person on the platform hears a trumpet play a note at 3520 Hz.DATA: vsound = 343 m/s a) What is the true frequency of the trumpet? b) What is the wavelength of the sound? c) If the trumpet plays the same note after passing the platform, what frequency would the person on the platform hear? a) 3300 Hz b) 9.74 cm c) 3106 Hz

  7. Shock Waves (Sonic Booms) When the source velocity exceeds the speed of sound,

  8. Application: speed radar

  9. Application: weather radar Both humidity (reflected intensity) and speed of clouds (doppler effect) are measured.

  10. Doppler Effect: Both Observer and Source Moving Switch appropriate signs if observer or source moves away

  11. Example 14.7 At rest, a car’s horn sounds the note A (440 Hz). The horn is sounded while the car moves down the street. A bicyclist moving in the same direction at 10 m/s hears a frequency of 415 Hz. DATA: vsound = 343 m/s. What is the speed of the car? (Assume the cyclist is behind the car) 31.3 m/s

  12. Example 14.8a A train has a whistle with a frequency of a 1000 Hz, as measured when both the train and observer are stationary. For a train moving in the positive x direction, which observer hears the highest frequency when the train is at position x=0? Observer A has velocity VA>0 and has position XA>0. Observer B has velocity VB>0 and has position XB<0. Observer C has velocity VC<0 and has position XC>0. Observer D has velocity VD<0 and has position XD<0.

  13. Example 14.8b A train has a whistle with a frequency of a 1000 Hz, as measured when both the train and observer are stationary. A train is moving in the positive x direction. When the train is at position x=0, An observer with V>0 and position X>0 hears a frequency: > 1000 Hz < 1000 Hz Can not be determined

  14. Example 14.8c A train has a whistle with a frequency of a 1000 Hz, as measured when both the train and observer are stationary. A train is moving in the positive x direction. When the train is at position x=0, An observer with V>0 and position X<0 hears a frequency: > 1000 Hz < 1000 Hz Can not be determined

  15. Example 14.8d A train has a whistle with a frequency of a 1000 Hz, as measured when both the train and observer are stationary. A train is moving in the positive x direction. When the train is at position x=0, An observer with V<0 and position X<0 hears a frequency: > 1000 Hz < 1000 Hz Can not be determined

  16. Standing Waves Consider a wave and its reflection:

  17. Standing Waves • Factorizes into x-piece and t-piece • Always ZERO at x=0 or x=ml/2

  18. Resonances Integral number of half wavelengths in length L

  19. Nodes and anti-nodes • A node is a minimum in the pattern • An antinode is a maximum

  20. 2nd harmonic 3rd harmonic Fundamental (n=1) Fundamental, 2nd, 3rd... Harmonics

  21. Example 14.9 A cello string vibrates in its fundamental mode with a frequency of 220 vibrations/s. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. a) Find the tension in the string b) Determine the frequency of the string when it vibrates in three segments. a) 163 Nb) 660 Hz

  22. Beats Interference from two waves with slightly differentfrequency

  23. Beat Frequency Derivation After time Tbeat, two sounds will differ by one complete cycle.

  24. Beats Demo

  25. Standing waves in Pipes - Open both ends Same expression for closed at both ends

  26. Standing waves in Pipes - Closed one end

  27. Example 14.10 An organ pipe of length 1.5 m is open at one end. What are the lowest two harmonic frequencies? DATA: Speed of sound = 343 m/s 57.2 Hz, 171.5 Hz

  28. Example 14.11 An organ pipe (open at one end and closed at the other) is designed to have a fundamental frequency of 440 Hz.Assuming the speed of sound is 343 m/s, a) What is the length of the pipe? b) What is the frequency of the next harmonic? a) 19.5 cm b) 1320 Hz

  29. Interference of Sound Waves Assume sources “a” and “b” are “coherent”. If observer is located ra and rb from the two sources, Source a Source b rb ra Observer

  30. Example 14.12 A pair of speakers separated by 1.75 m are driven by the same oscillator at a frequency of 686 Hz. An observer starts at one of the speakers and walks on a path that is perpendicular to the separation of the two speakers. (Assume vsound = 343 m/s) a) What is the position of the last intensity maximum? b) What is the position of the last intensity minimum? c) What is the position of the first intensity maximum? a) 2.81 m b) 6.00 m c) 27 cm

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