PHYSICS 231 Sound PHY 231

Transcription

1 PHYSICS 231 Sound 1

2 Sound: longitudinal waves A sound wave consist o longitudinal oscillations in the pressure o the medium that carries the sound wave. Thereore, in vacuum: there is no sound. 2

3 Relation between amplitude and intensity A x -A time (s) For sound, the intensity I goes linear with the amplitude o the longitudinal wave squared I~A 2 3

4 Intensity Intensity: rate o energy low through an area Power (P) J/s A (m 2 ) Intensity: I=P/A (J/m 2 s=w/m 2 ) Even i you have a powerul sound source (say a speaker), the intensity will be small when ar away. 4

5 Intensity and distance rom the source Sound rom a point source produces a spherical wave. Why does the sound get ainter urther away rom the source? 5

6 Intensity and distance r=1 I=P/(4r 2 )=P/(4) 1 r=2 I=P/(4r 2 )=P/(16) 4 r=3 I=P/(4r 2 )=P/(36) 9 The amount o energy passing through a spherical surace at distance r rom the source is constant, but the surace becomes larger. I 1 /I 2 =r 22 /r 1 2 I=Power/Surace=P/A=P/(4r 2 ) 6

7 Wave ronts sound emitted rom a point source are spherical. Far away rom that source, the wave are nearly plane. plane waves spherical waves 7

8 The speed o 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 material Air (20 o C) Helium Water Aluminum Diamond speed o sound 343 m/s 972 m/s 1493 m/s 5100 m/s m/s 8

9 Quick question The speed o sound in air is aected in changes in: a) wavelength b) requency c) temperature d) amplitude e) none o the above 9

10 Intensity Faintest sound we can hear: I~1x10-12 W/m 2 (1000 Hz) Loudest sound we can stand: I~1 W/m 2 (1000 Hz) sound wave vibrating ear drum Factor o 10 12? Loudness works logarithmic 10

11 sound/decibel level =10log(I/I 0 ) I 0 =10-12 W/m 2 y=log 10 x inverse o x=10 y (y=ln(x) x=e y ) log(ab) =log(a)+log(b) log(a/b) =log(a)-log(b) log(a n ) =nlog(a) 11

12 decibels =10log(I/I 0 ) I 0 =10-12 W/m 2 An increase o 10 db: intensity o the sound is multiplied by a actor o =10 10=10log(I 2 /I 0 )-10log(I 1 /I 0 ) 10=10log(I 2 /I 1 ) 1=log(I 2 /I 1 ) 10=I 2 /I 1 I 2 =10I 1 12

13 sound levels Table o sound levels L and corresponding sound pressure and sound intensity Sound Sources Examples with distance Sound Pressure Level L p dbspl Sound Pressure p N/m 2 = Pa Sound Intensity I W/m 2 Jet aircrat, 50 m away Threshold o pain Threshold o discomort Chainsaw, 1 m distance Disco, 1 m rom speaker Diesel truck, 10 m away Kerbside o busy road, 5 m Vacuum cleaner, distance 1 m Conversational speech, 1 m Average home Quiet library Quiet bedroom at night Background in TV studio Rustling leaves in the distance Threshold o hearing

14 Frequency vs intensity 1000 Hz 14

15 Example A person living at Cherry Lane (300 m rom the rail track) is tired o the noise o the passing trains and decides to move to Abbott (3.5 km rom the rail track). I the sound level o the trains was originally 70dB (vacuum cleaner), what is the sound level at Abbott? 15

16 example A machine produces sound with a level o 80dB. How many machines can you add beore exceeding 100dB? 16

17 PHYSICS 231 Doppler eect 17

18 Doppler eect: a non-moving source v sound =v sound / source you 18

19 doppler eect: a source moving towards you v source source you the distance between the wave ront is shortened v source v v sound vsound vsource prime : heard observable v sound v source The requency becomes larger: higher tone 19

20 doppler eect: a source moving away rom you the distance between the wave ront becomes longer you v source source v source v source v v v vsound : negative!!! sound sound v v source source The requency becomes lower: lower tone 20

21 doppler eect: you moving towards the source v sound additional waveronts detected per second : source you v observer v observer v observer v v sound sound 21

22 doppler eect: you moving away rom the source v sound source you additional waveronts detected per second : v observer v observer v : negative observer v observer v v sound sound 22

23 doppler eect: general source you v v v v observer source v observer : positive i moving towards to source v source : positive i moving towards the observer 23

24 question An ambulance is moving towards you with its sirens on. The requency o the sound you hear is than the requency you would hear i the ambulance were not moving at all. a) higher b) the same c) lower v v v v observer source 24

25 example A police car using its siren (requency 1200Hz) is driving west towards you over Grand River with a velocity o 25m/s. You are driving east over grand river, also with 25m/s. a)what is the requency o the sound rom the siren that you hear? b) What would happen i you were also driving west (behind the ambulance)? v sound =343 m/s a) b) 25

26 applications o doppler eect: weather radar Both humidity (relected intensity) and speed o clouds (doppler eect) are measured. 26

27 shock waves v v v v observer source what happens i v source v sound? vt sin=v sound /v source v source > v sound waveront: high pressure wave that carries a lot o energy 27

28 shock waves: passing jet 28

29 applications o the doppler eect: speed radar v v v v observer source v v v approachingcar 29

30 example 300m you 1000m jet A low-lying jet passes by at 300m away rom you. When it is 1 km urther, you hear the sonic shock-wave. What was the speed o the jet in mach? 30

31 PHYSICS 231 String instruments 31

32 standing wave v 1 v 2 i two waves travel in opposite directions and v 1 =v 2, the superposition o the two waves produces a standing wave: maxima and minima always appear at the same location 32

33 standing waves in a guitar string waves in the string travel back and orth and create standing waves. a wave bouncing back rom a ixed point, returns inverted 33

34 we can produce dierent wave lengths L L L 1 =2L 2 =L 3 =2L/3 L L 4 =2L/4 5 =2L/5 both ends ixed n =2L/n or L=n n /2 34

35 standing waves both ends ixed n =2L/n or L=n n /2 n n v 1 2 n nv 2L v 2L 2v 2L nv 2L n 1 n 2L F 1 : undamental requency nth harmonics F: tension in rope : mass per unit length 35

36 example: the guitar n th harmonics: depends where and how the string is struck note that several harmonics can be present and that non-harmonics are washed out n n 2L F tension can be varied by stretching the wire changes rom string to string: bass string is very heavy length can be chosen by placing ingers 36

37 beats Superposition o 2 waves with slightly dierent requency The amplitude changes as a unction o time, so the intensity o sound changes as a unction o time. The beat requency (number o intensity maxima/minima per second): beat = a - b 37

38 example A guitar string is struck. Assume that the irst harmonic is only excited. What happens to the requency i: a) The player put a inger at hal the length o the string? b) The player makes the tension 10% larger (by turning the tuning screw)? c) A string is struck in the same way, but its mass is 3 times higher? 38

39 example Someone is trying to tune a guitar. One o the strings is supposed to have a requency o 500 Hz. The person is using a tuning ork which produces a sound o exactly this requency, but while sounding the ork and the playing the guitar, hears a beat in the sound with a requency o 3 Hz (3 beat per second). a) What is the real requency o the guitar string? b) By what raction does the person need to change the tension o the guitar string to tune it properly? 39