Chapter 14

1 Chapter 14 Sound1 Sound Waves Sound is longitudinal pressure (compression) waves Range of hearing: 20 Hz to 20,000 HzFREQUENCY DEMO2 Speed of SoundLiquids and Gases: B is bulkmodulus, ! is mass/volumeSolids: Y is Young s modulus331 m/s is v at 0 C;T is the absolute !v=Y!vair=(331ms)T273K3 Example Brown hits a steel railroad rail with a Brown, standing one mile down the track, hearsthe bang through the cool 32 F air while her twin sister Boopsie is lying next to her and hears the bang through the steel by placing her ear on the : Ysteel= Pa, !steel=7850 kg/m3 What is the time difference between the moments when Betsy and Boopsie hear the bang? s4 Intensity of Sound WavesSI units are W/m2 PowerAreaIntensity is proportional to squareof amplitude (pressure modulation)I=!EA!t=PA5 Intensity Range for Human HearingThreshold of Hearing 10-12 W/m2 "P ~ 10-10 atm !

2 Threshold of Pain W/m26 Decibel ScaleSensation is logarithmic I0 is threshold of hearing (0 dB) Threshold of Pain is therefore 120 dB!=10log10 IIoI=I010!/107 Intensity vs. Intensity Level INTENSITY is P/A, W/m2 INTENSITY LEVEL is in decibels (dimensionless)8 Sound Level Demo9 Example noisy machine in a factory produces a sound with a level of 80 dB. How many machines can the factory house without exceeding the 100-dB limit? a) machinesb) 20 machinesc) 100 machines10 Spherical WavesEnergy propagates equally in all directions#I=P4!r2I1I2=r22r1211 Example (skip)A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 50 dB by an observer 10 km away. Treating the horn as a point source and neglect any absorption of sound by the air or ground,a) What is the average power generated by the horn? b) What intensity level of the horn s sound is observed by someone waiting at an intersection 50 m from the train?

3 A) 126 Wb) 96 dB12 Example Bob buys a 20-W train whistle and figures out that he won t have any trouble standing 2 meters from the whistle since his stereo speakers are rated at 100 W and he has little trouble with the speakers turned all the way up. What is the intensity level of the whistle?116 dB13 Doppler EffectA change in the frequency experienced by an observer due to motion of either the observer or the DEMO14 Doppler Effect, Moving ObserverWhen not moving,When moving, f=v!f'=(v+vobs)! '= v+vov!"#$%&15If observer moves away: '= v!vov"#$%&'16 Example is riding a roller coaster. Her mother who is standing on the ground behind her yells out to her at a frequency of 1000 Hz, but it sounds like 920 Hz.(v=343 m/s)What is Mary s speed? m/s17 Doppler EffectSource in Motion!'=!"vsT=!"vs!v=!1"vsv()f'=v!'f'=f vv!vs18 Doppler Effect, Source in MotionApproaching source:Source leaving:f'=fvv!

4 Vsf'=fvv+vs19 Example train has a brass band playing a song on a flatcar. As the train approaches the station at m/s, a person on the platform hears a trumpet play a note at 3520 : 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 Hzb) cmc) 3106 Hz20 Shock Waves (Sonic Booms)When the source velocity approaches the speed of sound,21 Application: speed radar22 Application: weather radar Both humidity (reflected intensity) and speed of clouds(doppler effect) are Effect: Both Observer and Source MovingSwitch appropriate signs if observer or source moves away '= v vov vs!"#$%&24 Example rest, a car s horn sounds the note A (440 Hz). The horn is sounded while the car moves down the street.

5 A bicyclist moving in the same direction at 10 m/s hears a frequency of 415 Hz. DATA: vsound = 343 is the speed of the car? (Assume the cyclist is behind the car) m/s25 Example train has a whistle with a frequency of a 1000 Hz, as measured when the 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= A has velocity VA>0 and has position XA> B has velocity VB>0 and has position XB< C has velocity VC<0 and has position XC> D has velocity VD<0 and has position XD< train has a whistle with a frequency of a 1000 Hz, as measured when the 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= observer with V>0 and position X>0 hears a frequency:a)> 1000 Hzb)< 1000 Hzc)Can not be determined27 Example train has a whistle with a frequency of a 1000 Hz, as measured when the both the train and observer are stationary.

6 For a train moving in the positive x direction, which observer hears the highest frequency when the train is at position x= observer with V>0 and position X<0 hears a frequency:a)> 1000 Hzb)< 1000 Hzc)Can not be determined28 Example train has a whistle with a frequency of a 1000 Hz, as measured when the 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= observer with V<0 and position X<0 hears a frequency:a)> 1000 Hzb)< 1000 Hzc)Can not be determined29 Standing WavesConsider a wave and its reflection:yright=Asin2!x"#ft$%&'()*+, !x"$%&'()cos2!ft#cos2!x"$%&'()sin2!ft012 345yleft=Asin2!x"+ft$%&'()*+, !x"$%&'()cos2!ft+cos2!x"$%&'()sin2!ft012 345yright+yleft=2 Asin2!x"$%&'()cos2!ft30 Standing Waves Factorizes into x-piece and t-piece Always ZERO at x=0 or x=m$/2yright+yleft=2 Asin2!

7 X"#$%&'(cos2!ft31 ResonancesIntegral number of half wavelengths in length Ln!2=L32 Resonance in String Demo33 Nodes and anti-nodes A node is a minimum in the pattern An antinode is a maximum34 Fundamental, 2nd, HarmonicsFundamental (n=1)2nd harmonic3rd harmonicn!2=L35 Example cello string vibrates in its fundamental mode with a frequency of 220 vibrations/s. The vibrating segment is cm long and has a mass of ) Find the tension in the stringb) Determine the frequency of the string when it vibrates in three segments. a) 163 Nb) 660 Hz36 Loose Ends(Organ pipes open at one end)L=2n+1()!4L=!4L=3!4L=5!437 Example organ pipe of length m is open at one end and closed at the other. What are the lowest two harmonic frequencies?DATA: Speed of sound = 343 Hz, Hz38 BeatsInterference from two waves with slightly differentfrequency39 Beat Frequency DerivationAfter time Tbeat, two sounds will differ by one complete !

8 N2=1f1 Tbeat!f2 Tbeat=1 Tbeat=1f1!f2fbeat=1 Tbeatfbeat=f1!f240 Beats Demo41 Standing Waves in Air Columns42 Tube Closed at One End!n=(2n+1)!443 Tube Open at Both EndsSame expression for closed at both ends!n=n!244 Resonance Demos1. Pipe2. Bridge45 Example organ pipe (open at one end and closed at the other) is designed to have a fundamental frequency of 440 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) cmb) 1320 Hz46 Interference of Sound WavesAssume sources a and b are coherent . If observer is located ra and rb from the two sources,ra!rb=n"formaximumra!rb=(n+12)"f orminimumrarbSource aSource bObserver47 Example ) mb) mc) 27 cmTe A pair of speakers separated by 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.

9 (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 xt48