HW assignment. Interference. From last time. Destructive Interference in a String. Question. Interference of sound waves

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1 HW assignment M Chap 7: Question D G Chap 15: Q14, Q18 G Chap 12: Q18, Q20, E4, E10 From last time Wavelength, frequency, and velocity are all related. Waves can add up, either giving a wave of larger amplitude, or one of smaller amplitude. Interference Water drop is a source of circular waves (twodimensions here) When the waves overlap, they superimpose. In some areas they cancel, in others they reinforce. This is called Wed. Feb 15, 2006 Phy107 Lecture 12 1 Wed. Feb 15, 2006 Phy107 Lecture 12 2 Constructive Interference in a String Two pulses are traveling in opposite directions The net displacement when they overlap is the sum of the displacements of the pulses Note that the pulses are unchanged after the Destructive Interference in a String Two pulses are traveling in opposite directions The net displacement when they overlap the displacements of the pulses subtract Note that the pulses are unchanged after the Wed. Feb 15, 2006 Phy107 Lecture 12 3 Wed. Feb 15, 2006 Phy107 Lecture 12 4 Question Below are sound waves to be added together. Which set results in a quieter sound? A. A B. B C. Both same B Interference of sound waves Interference arises when waves change their phase relationship. Can vary phase relationship of two waves by changing physical location of speaker. in-phase 1/2 λ phase diff A Wed. Feb 15, 2006 Phy107 Lecture 12 5 Constructive Destructive Wed. Feb 15, 2006 Phy107 Lecture

2 Superimposing sound waves Depending on your relative distance from two identical sound sources, the sound intensity can vary. Important aspect is relative distance from each source in wavelengths! crest trough Interference of 2 speakers destructive quit tone constructive,loud tone Wed. Feb 15, 2006 Phy107 Lecture 12 7 Wed. Feb 15, 2006 Phy107 Lecture 12 8 Interference engineering Line array works by Off-axis sound canceled by on the vertical axis. Horizontal plane unaffected Total sound intensity drops off more slowly Wed. Feb 15, 2006 Phy107 Lecture 12 9 Wed. Feb 15, 2006 Phy107 Lecture Destructive Two speakers playing the same tone together can be quieter each than individually! Question Two speakers in different corners of your room play identical tones of 340 Hz. You are at different distances from the two speakers. At what difference in distances do the sound waves cancel 1/2 wavelength phase diff Destructive Destructive for frequencies such that path length difference is 1/2 wavelength. A. 1.0 m B. 0.5 m C Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture

3 Interference summary Important quantity is distance difference in number of wavelengths. A distance difference of a half wavelength leads to destructive. Whole wavelength differences lead to constructive. But destructive also for 3 half wavelengths, 5 half-wavelengths, etc. Constructive also occurs at differences of 2 whole wavelengths, 3 whole wavelengths Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. For instance, a fire engine or train passing you. 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 Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Doppler Effect for a moving source As the source moves toward the observer (A), the wavelength appears shorter and the frequency increases As the source moves away from the observer (B), the wavelength appears longer and the frequency appears to be lower Question If the buzzer had a lower frequency, how would the the shift in frequency that you hear change? A. bigger shift B Smaller shift C shift stays the same Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Shock Waves and Sonic Booms 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 Fig 14.11, p. 439 Slide 15 Sonic Boom Source of sound approaching the listener is equal to or faster than the speed of sound Each successive wave is superimposed on the previous one Shock wave results as air compression in crest gets very large Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture

4 Breaking the sound barrier No sound received till after the source passes the listener - then a sonic boom - followed by normal sound from the source Conical bow wake from condensed water vapor at high pressure shock wave front. Breaking the sound barrier in a canoe! If the canoe moves faster than the water wave velocity, shock wave also builds up where all the crests line up. For water wave velocity ~1 m/s, so Mach 2 is 2 m/s = 4.5 mph!! Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Resonance So far have been talking about waves traveling in media that extend in all directions. In a finite object, the boundaries cause reflections. The reflected wave interferes with rest of wave, causing destructive or constructive. For destructive, the wave tends to die away. But for constructive, the wave builds up. Which one happens depends on wavelength. Most objects resonate But even complicated objects have some natural frequency of oscillation Pendulum Wine glass Musical instruments Natural frequency has to do with size and materials properties of object. Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Closed tube resonance The different length wood blocks resonate at different wavelengths, producing different frequency sound waves. Striking the block with a mallet produces waves of many different wavelengths in the block. Reflections from the ends interfere destructively for all but the natural frequencies. Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture

5 Air column in typical wind instrument Half wave fits in to column and creates fundamental If all holes are covered, this recorder is long If first few are open, the effective length is shorter Wind instruments play different notes by changing their length L L Plucking or bowing can be used to start a string oscillating Bowing a string transfers energy gradually Rhythmic excitation at the right frequency causes sympathetic vibration Bowing always excites string at the right frequency The longer the string s resonance lasts, the more effective the gradual energy transfer Plucking a string transfers energy instantly Excited modes depend on where you pluck Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Resonance on string First three natural vibrational modes of a string fixed at both ends (e.g. a guitar string). A normal pluck excites primarily the first vibrational mode. Wine glass resonances Stroboscopic movie of fundamental vibration mode of a wineglass. Holographic interferometry showing contour map of vibration for different modes. Points of maximum motion appear as bull s eyes. Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture Ben Franklin "Of all my inventions, the glass armonica has given me the greatest personal satisfaction." - Ben Franklin The glass armonica was one of the most celebrated instruments of the 18th century. Composers such as Beethoven, Mozart, and Donizetti would write music for the armonica. Wed. Feb 15, 2006 Phy107 Lecture Mozart wrote two pieces for the armonica, including "Adagio and Rondo 617," and Beethoven wrote a melodrama with a narrator accompanied by armonica. Armonica performers complained that the instrument was upsetting them emotionally. They said that the vibrations were entering their fingertips and causing mental anguish. Maybe lead poisoning from lead in the glass hemispheres of the instrument. Wed. Feb 15, 2006 Phy107 Lecture

6 Driving at resonance Can tune a speaker to the fundamental resonant frequency of the wine glass (here 1210 Hz). More and more energy poured into glass - the glass vibrates with larger and larger amplitude. The glass shatters as the vibration amplitude becomes too large. Tacoma Narrows Bridge Even a non-resonant drive can transfer energy. Driven by 40 mph wind Causes vibration of bridge at its natural (resonant) frequency. Movie of bridge torsional vibrations Wed. Feb 15, 2006 Phy107 Lecture Wed. Feb 15, 2006 Phy107 Lecture