MusicPAL #9 SoundSlide 3HarmonicsThe Decibel ScaleSound LevelsThe Doppler EffectFrequency ChangeGeneral Doppler EffectNext TimeConsider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium through which it passes to maximize its speed?Consider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium to maximize its pressure amplitude?If you were producing the sound with a speaker, as you changed the medium to increase the pressure amplitude, does driving the speaker become harder, easier or stay the same?If the density of air doubles (with no other changes) what happens to the intensity of sound in that air?Consider two sound detectors. Detector A is 1 meter away from a sound source and detector B is 3 meters away. If each detector receives the same amount of energy per second, what is the ratio of the areas of the detectors (area A/area B)?Summary: Sound WavesSummary: Wave EquationsSummary: Intensity and MusicSummary: Doppler EffectMusicPhysics 202Professor Lee CarknerLecture 9PAL #9 SoundInterference from two loudspeakersTo get destructive interference you want the received waves to be out of phase by ½ wavelength f = 1150 Hz, v = 343 m/s (for room temperature air)v = f, = v/f = 343/1150 = 0.3 m If L1 is 4m, make L2 4.15 m L2 = 4 m (or 4.3 m or 3.7 m etc.)MusicWe shall consider an generalized instrument consisting of a pipe which may be open at one or both ends There will always be a node at the closed end and an anti-node at the open endHarmonics For resonance need a integer number of ½ wavelengths to fit in the pipe L = ½ n v = ff = nv/2Ln = 1,2,3,4 … For resonance need an integer number of ¼ wavelengths to fit in the pipe L = ¼ n v = ff = nv/4Ln = 1,3,5,7 … (only have odd harmonics)The Decibel Scale To model ear’s logarithmic response, we use the decibel scale = (10 dB) log (I/I0) I0 = 10-12 W/m2 (at the threshold of human hearing) 10 times louder means 10 dB greater levelSound Levels A pain level sound is a trillion times as intense as a sound you can barely hearYour hearing response is logarithmicA sound 10 times as intense sounds twice as loudHearing Threshold Whisper Talking Rock Concert Pain120 dBThe Doppler Effect If there is any relative motion between the two, the frequency of sound detected will differ from the frequency of sound emittedFrequency ChangeIf the source and the detector are moving closer together the frequency increases If the source and the detector are moving further apart the frequency decreasesGeneral Doppler Effect f’ = f ( v±vD / v±vS )What sign should be used? Do this twice to find the numerator and denominator signFor motion tow ard, the sign should be chosen to increase f’ Remember that the speed of sound (v) will often be 343 m/sNext TimeRead: 18.1-18.6Consider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium through which it passes to maximize its speed? a) Increase , increase Bb) Increase , decrease Bc) Decrease , increase Bd) Decrease , decrease Be) Speed will only change if we change the frequencyConsider a sound wave with a fixed amplitude and frequency. How would you change the properties of the medium to maximize its pressure amplitude? a) Increase , increase Bb) Increase , decrease Bc) Decrease , increase Bd) Decrease , decrease Be) Speed will only change if we change the frequencyIf you were producing the sound with a speaker, as you changed the medium toincrease the pressure amplitude, does driving the speaker become harder, easier or stay the same?a) Harderb) Easierc) Stay the sameIf the density of air doubles (with no other changes) what happens to the intensity of sound in that air? a) Decreases by square root of 2b) Decreases by factor of 2c) Stays the samed) Doublese) Increases by square root of 2Consider two sound detectors. Detector A is 1 meter away from a sound source and detector B is 3 meters away. If each detector receives the same amount of energy per second, what is the ratio of the areas of the detectors (area A/area B)?a) 1/9b) 1/3c) 1d) 3e) 9Summary: Sound WavesSound waves are longitudinal or pressure wavesThe medium oscillates in the direction of travelThe speed of sound depends on the density and the bulk modulus (compressibility ) of the medium:v = (B/)½Summary: Wave EquationsThe equations for the amplitude and pressure of a sound wave are:s = sm cos (kx-t)p = pm sin (kx-t)pm = (v) smWaves from two sources will interfere based on the path length difference between the sources and detectorL = m (fully constructive)L = (m+½) (fully destructive)Summary: Intensity and MusicThe intensity of sound falls off with a inverse square law:I = Ps/4r2I =½v2sm2The sound level is: = (10 dB) log (I0/I)Harmonic frequencies of a pipef = nv/2L (open at 2 ends)f = nv/4L (open at 1 end)Beat frequency = fbeat = f1 - f2Summary: Doppler EffectRelative motion together produces an increase in frequencyRelative motion apart produces a decrease in frequencyf’ = f ( v±vD / v±vS
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