PHYSICS 231 Lecture 31 interference sound PHY 231 1 Final Exam Alternative Exam Monday Dec 14 9 00am 11 00am morning NSCL seminar room Regular Exam Tuesday Dec 15 5 45pm 7 45pm evening W ll Hall Wells H ll B 108 B 108 PHY 231 2 Interference Two traveling waves pass through each other without affecting each other The resulting displacement is the superposition of the two individual waves waves example two pulses on a string that meet PHY 231 3 Interference II constructive interference destructive interference4 PHY 231 demo interference Interference III constructive t ti iinterference t f waves in phase destructive interference waves out of phase 5 PHY 231 Interference IV Two interfering waves can at times constructively interfere and at times destructively interfere If the two interfering waves always have the same vertical displacement at any point along the waves but are of opposite sign standing waves later more PHY 231 6 Interference holds for any wave type The pulses can be sine waves rectangular waves or triangular waves PHY 231 7 Interference in spherical waves m xim m of maximum f wave r r 1 2 minimum i i of f wave r1 r2 positive constructive interference negative constructive interference destructive interference if r2 rr1 n n if r2 r1 n n 0 1 2 3 then constructive interference occurs then destructive interference occurs PHY 231 8 Interference of water waves PHY 231 9 Example ttwo speakers k separated t d by b 0 0 7m 7 produce d a sound with frequency 690 Hz from d2 the same sound system y 0 7m 0 7m A person starts walking from one of the d1 speakers perpendicular to the line direction of connecting the speakers speakers After what walking person distance does he reach the first maximum And the first minimum vsound 343 343 m s v f so v f 343 690 0 5m 1st maximum d1 d2 1 0 5 d2 0 72 d12 d1 0 72 d12 0 5 d1 0 24m 1st minimum d1 d2 0 25 d1 0 7 0 72 d12 0 25 0 25 d1 0 855 0 855 PHY 231 10 quiz extra credit maximum of wave r1 r2 minimum of wave r1 r2 Two sources produce coherent sound in phase Along the line r1 r2 interference occurs a constructive positive or negative b destructive c only constructive positive d only l constructive t ti negative ti if r2 r1 n then constructive interference occurs 11 PHY 231 if r2 r1 n the destructive interference occurs Reflection of waves Frope on wall Fwall on rope demo rope on wall FIXED END pulse inversion PHY 231 FREE END no inversion 12 Connecting ropes If a pulse travels from a light rope to a heavy rope light the boundary is li h heavy h nearly fixed The pulse is partially reflected inverted and d partially ti ll ttransmitted itt d Ain before AR AR Ain AT Ain If a pulse travels from a heavy rope to a light rope light heavy the boundary is nearly free The pulse is partially reflected not inverted and partially transmitted before Ain AR AT AT after PHY 231 AR Ain AT Ain after 13 Sound longitudinal waves PHY 231 14 The speed of sound Depends on the how easy the material is compressed elastic property and how much the material resists acceleration inertial property v elastic property inertial property v B B bulk modulus density The velocity also depends on temperature In air v 331 T 273 K so v 343 m s at room temperature PHY 231 15 Quiz The speed of sound in air is affected in changes in a wavelength b frequency f c temperature d amplitude p e none of the above PHY 231 16 Intensity Intensity rate of energy flow through an area Power P J s A m2 I P A J m2s W m2 example If you buy a speaker it gives power output in Watts However even if you put a powerful speaker in a large room the intensity of the sound can be small PHY 231 17 Intensity Faintest sound we can hear I 1x10 12 W m2 1000 Hz H Loudest sound we can stand I 1 W m2 1000 Hz Factor of 1012 Loudness works logarithmic g PHY 231 18 decibel level 10log I I0 sound level dB y log10x log ab log a b log an I0 10 12 W m2 inverse of x 10y log a log b log a log b nlog a y ln x x ey 2 1 10 log I g 2 I1 120 100 80 60 40 20 0 10 12 10 11 10 10 10 9 10 8 10 7 10 6 PHY 231 10 5 10 4 10 3 10 2 10 1 1 2 Intensity I W m 19 decibels 10log I I0 I0 10 12 W m2 An increase of 10 dB intensity of the sound is multiplied by a factor of 10 2 1 10 10 10log I2 I0 10log I1 I0 10 10log I2 I1 1 log I2 I1 10 I 10 I2 I1 I2 10I1 2 1 10 log I 10 log I2 I1 PHY 231 20 Frequency vs intensity 1000 Hz PHY 231 21 example A machine produces sound with a level of 80dB 80dB How many machines can you add before exceeding 100dB 1 machine 80 dB 10log I I0 8 log I I0 log I 1E 12 108 I 1E 12 I 1E 12 I1 10 4 W m2 machines 100 dB 10log I I0 10 log I I0 log I 1E 12 1010 I 1E 12 I 10 2 W m2 I1 I 10 4 10 2 1 100 The intensity must increase by a factor of 100 one needs to add 99 machines PHY 231 22
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