Chapter 1717.1 The Principle of Linear SuperpositionSlide 3Slide 417.2 Constructive and Destructive Interference of Sound WavesSlide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 1217.3 DiffractionSlide 14Slide 1517.4 BeatsSlide 1717.5 Transverse Standing WavesSlide 19Slide 20Slide 21Slide 2217.6 Longitudinal Standing WavesSlide 24Slide 25Slide 26Slide 2717.7 Complex Sound WavesSlide 29Chapter 17The Principle of Linear Superposition and Interference Phenomena17.1 The Principle of Linear SuperpositionWhen the pulses merge, the Slinkyassumes a shape that is the sum ofthe shapes of the individual pulses.17.1 The Principle of Linear SuperpositionWhen the pulses merge, the Slinkyassumes a shape that is the sum ofthe shapes of the individual pulses.17.1 The Principle of Linear SuperpositionTHE PRINCIPLE OF LINEAR SUPERPOSITIONWhen two or more waves are present simultaneously at the same place,the resultant disturbance is the sum of the disturbances from the individualwaves.17.2 Constructive and Destructive Interference of Sound WavesWhen two waves always meet condensation-to-condensation and rarefaction-to-rarefaction, they are said to be exactly in phase and to exhibit constructive interference.17.2 Constructive and Destructive Interference of Sound WavesWhen two waves always meet condensation-to-rarefaction, they are said to be exactly out of phase and to exhibit destructive interference.17.2 Constructive and Destructive Interference of Sound Waves17.2 Constructive and Destructive Interference of Sound WavesIf the wave patters do not shift relative to one another as time passes,the sources are said to be coherent.For two wave sources vibrating in phase, a difference in path lengths thatis zero or an integer number (1, 2, 3, . . ) of wavelengths leads to constructive interference; a difference in path lengths that is a half-integer number(½ , 1 ½, 2 ½, . .) of wavelengths leads to destructive interference.17.2 Constructive and Destructive Interference of Sound WavesExample 1 What Does a Listener Hear?Two in-phase loudspeakers, A and B, are separated by 3.20 m. A listener is stationedat C, which is 2.40 m in front of speaker B.Both speakers are playing identical 214-Hz tones, and the speed of sound is 343 m/s.Does the listener hear a loud sound, or no sound?17.2 Constructive and Destructive Interference of Sound WavesCalculate the path length difference.   m 1.60m 40.2m 40.2m 20.322Calculate the wavelength.m 60.1Hz 214sm343fvBecause the path length difference is equal to an integer (1) number of wavelengths, there is constructive interference, whichmeans there is a loud sound.17.2 Constructive and Destructive Interference of Sound WavesConceptual Example 2 Out-Of-Phase SpeakersTo make a speaker operate, two wires must be connected between the speaker and the amplifier. To ensure that the diaphragms of the two speakers vibrate in phase, it is necessary to make these connectionsin exactly the same way. If the wires for onespeaker are not connected just as they are for the other, the diaphragms will vibrateout of phase. Suppose in the figures (next slide), the connections are made so that the speakerdiaphragms vibrate out of phase, everythingelse remaining the same. In each case, what kind of interference would result in the overlap point?17.2 Constructive and Destructive Interference of Sound Waves17.3 DiffractionThe bending of a wave aroundan obstacle or the edges of anopening is called diffraction.17.3 DiffractionDsinsingle slit – first minimum17.3 DiffractionD22.1sin Circular opening – first minimum17.4 BeatsTwo overlapping waves with slightly different frequencies gives rise to the phenomena of beats.17.4 BeatsThe beat frequency is the difference between the two soundfrequencies.17.5 Transverse Standing WavesTransverse standing wave patters.17.5 Transverse Standing WavesIn reflecting from the wall, aforward-traveling half-cyclebecomes a backward-travelinghalf-cycle that is inverted.Unless the timing is right, thenewly formed and reflected cyclestend to offset one another.Repeated reinforcement betweennewly created and reflected cyclescauses a large amplitude standingwave to develop.17.5 Transverse Standing Waves,4,3,2,1 2 nLvnfnString fixed at both ends17.5 Transverse Standing Waves,4,3,2,1 2 nLvnfn17.5 Transverse Standing WavesConceptual Example 5 The Frets on a GuitarFrets allow a the player to produce a complete sequence of musical noteson a single string. Starting with the fret at the top of the neck, each successivefret shows where the player should press to get the next note in the sequence.Musicians call the sequence the chromatic scale, and every thirteenth note in it corresponds to one octave, or a doubling of the sound frequency. The spacing between the frets is greatest at the top of the neck and decreases witheach additional fret further on down. Why does the spacing decrease going down the neck?17.6 Longitudinal Standing WavesA longitudinal standing wave pattern on a slinky.17.6 Longitudinal Standing Waves,4,3,2,1 2 nLvnfnTube open at both ends17.6 Longitudinal Standing WavesExample 6 Playing a FluteWhen all the holes are closed on one type offlute, the lowest note it can sound is middleC (261.6 Hz). If the speed of sound is 343 m/s,and the flute is assumed to be a cylinder openat both ends, determine the distance L.17.6 Longitudinal Standing Waves,4,3,2,1 2 nLvnfn  m 656.0Hz 261.62sm34312 nfnvL17.6 Longitudinal Standing Waves,5,3,1 4 nLvnfnTube open at one end17.7 Complex Sound Waves17.7 Complex Sound