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Wave - III

Wave - III. Sound Resonances. Harmonics:. Consider a pipe of length L , open at one end , closed at the other end. At resonance, a displacement antinode at the open end , and a displacement node at the closed end. The longest wavelength to satisfy this condition is.

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Wave - III

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  1. Wave - III

  2. Sound Resonances Harmonics: Consider a pipe of length L, open at one end, closed at the other end. At resonance, a displacement antinode at the open end, and a displacement node at the closed end. The longest wavelength to satisfy this condition is Fundamental resonant frequency

  3. In both cases: Pipe open at both ends: displacement antinodes at both ends. open endclosed at the other end. Pipe closed at both ends: displacement nodes at both ends. The same expression as in string with both ends fixed.

  4. Consider Very small ≈w1≈w2 Beats Two sound waves with different but close frequencies give rise to BEATS

  5. On top of the almost same frequency, the amplitude takes maximum twice in a cycle: cosw’t = 1 and -1: Beats Beat frequencyfbeat:

  6. The Doppler Effect The Doppler Effect: the frequency change related to the motions of the source or/and detector In the following, the speed is measured with respect tothe air, through which the sound wave travels

  7. Divided by l to get the number of periods in time t Distance the sound travels in time t Periods in unit time: frequency Detector Moving, Source Stationary Thedetector stationary: Thedetector moving toward the source: more periods reaches detector. Equivalently:

  8. In general: + : toward S -: away from S Thedetector moving toward the source: vD is the SPEED, always positive

  9. The source stationary: Distance between two wavefronts period T apart The source moving toward the detector : waves are squeezed. Equivalently: Source Moving, Detector Stationary

  10. The source movingtoward the detector : vS is the SPEED, always positive In general: -: toward D +: away fromD

  11. + : toward S -: away from S +: away from D -: toward D In General All speeds are measured with respect to the medium of propagation: the air

  12. + : toward each other -: away from each other Relative speed: At Low Speed

  13. Supersonic Speed When vS>v, the equation no longer applicable: Supersonic speed The wavefronts form a Mach Cone A Shock Waveis generated: abrupt change of air pressure The source movingtoward the detector :

  14. HRW 51E(5th ed.).The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 686 Hz is held just over the open top end of the tube. At what positions of the water level will there be a resonance? Let L be the length of the air column. Then the condition for resonance is:

  15. HRW 61E(5th ed.).A tuning fork of unknown frequency makes three beats per second with a standard fork of frequency 384 Hz. The beat frequency decreases when a small piece of wax in put on a prong of the first fork. What is the frequency of this fork? fbeat = 3 Hz f1 = 381 or 387 Hz Resonant frequency Mass increases  f1 decreases fbeat decreases  f1 becomes closer to 384 Hz Therefore, f1 = 387 Hz

  16. HRW 68E(5th ed.). The 16,000 Hz whine of the turbines in the jet engines of an aircraft moving with speed 200 m/s is heard at what frequency by the pilot of a second aircraft trying to overtake the first at a speed of 250 m/s? The detector moves toward the source: take the plus sign for vD. The source moves away from the detector : take the plus sign for vS.

  17. (a) The source moving toward the detector : (b) The person (detector) moves toward the source at the wall with f’ = 467 Hz: HRW 80P(5th ed.).A person on a railroad car blows a trumpet note at 440 Hz. The car is moving toward a wall at 20.0 m/s. Calculate (a) the frequency of the sound as received at the wall and (b) the frequency of the reflected sound arriving back at the source.

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