PHYSICS 231 Sound PHY 231

Transcription

1 PHYSICS 231 Sound 1

2 Travelling (transverse) waves The wave moves to the right, but each point makes a simple harmonic vertical motion oscillation position y position x wave Since the oscillation is in the direction perpendicular (transverse) to the travelling wave, this is called a transverse wave example: water wave 2

3 Types of waves The wave moves to the right, but each point makes a simple harmonic horizontal motion wave oscillation Longitudinal wave : movement is in the direction of the wave motion. example: sound wave 3

4 describing a traveling wave : wavelength = length (m) of one oscillation. T: period = time for one oscillation T=1/f f: frequency (Hz) While the wave has traveled one wavelength, each point on the wave has made one period of oscillation. v=x/t=/t= f 4

5 example A traveling transverse wave is seen to have horizontal distance of 2m between a maximum and the nearest minimum and vertical height of 3m. If it moves with 1m/s, what is its: a) amplitude b) period c) frequency 5

6 sea waves An anchored fishing boat is going up and down with the waves. It reaches a maximum height every 5 seconds and a person on the boat sees that while reaching a maximum, the previous wave has moved about 40 m away from the boat. What is the speed of the traveling waves? 6

7 Sound: longitudinal waves A sound wave consist of longitudinal oscillations in the pressure of the medium that carries the sound wave. Therefore, in vacuum: there is no sound. 7

8 Relation between amplitude and intensity A x -A time (s) For sound, the intensity I goes linear with the amplitude of the longitudinal wave squared I~A 2 8

9 Intensity Intensity: rate of energy flow through an area Power (P) J/s A (m 2 ) Intensity: I=P/A (J/m 2 s=w/m 2 ) Even if you have a powerful sound source (say a speaker), the intensity will be small when far away. 9

10 Intensity and distance from the source Sound from a point source produces a spherical wave. Why does the sound get fainter further away from the source? 10

11 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 of energy passing through a spherical surface at distance r from the source is constant, but the surface becomes larger. I 1 /I 2 =r 22 /r 1 2 I=Power/Surface=P/A=P/(4r 2 ) 11

12 Wave fronts sound emitted from a point source are spherical. Far away from that source, the wave are nearly plane. plane waves spherical waves 12

13 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 material Air (20 o C) Helium Water Aluminum Diamond speed of sound 343 m/s 972 m/s 1493 m/s 5100 m/s m/s 13

14 Quick question The speed of sound in air is affected in changes in: a) wavelength b) frequency c) temperature d) amplitude e) none of the above 14

15 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 of 10 12? Loudness works logarithmic 15

16 sound/decibel level =10log(I/I 0 ) I 0 =10-12 W/m 2 y=log 10 x inverse of 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) 16

17 decibels =10log(I/I 0 ) I 0 =10-12 W/m 2 An increase of 10 db: intensity of the sound is multiplied by a factor of =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 17

18 sound levels Table of 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 aircraft, 50 m away Threshold of pain Threshold of discomfort Chainsaw, 1 m distance Disco, 1 m from speaker Diesel truck, 10 m away Kerbside of 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 of hearing

19 Frequency vs intensity 1000 Hz 19

20 Example A person living at Cherry Lane (300 m from the rail track) is tired of the noise of the passing trains and decides to move to Abbott (3.5 km from the rail track). If the sound level of the trains was originally 70dB (vacuum cleaner), what is the sound level at Abbott? 20

21 example A machine produces sound with a level of 80dB. How many machines can you add before exceeding 100dB? 21

22 PHYSICS 231 Doppler effect 22

23 Doppler effect: a non-moving source v sound f=v sound / source you 23

24 doppler effect: a source moving towards you v source source you the distance between the wave front is shortened v source f v v sound f f vsound vsource prime : heard observable v sound f v source f The frequency becomes larger: higher tone 24

25 doppler effect: a source moving away from you the distance between the wave front becomes longer you v source source f v source v source f v v v f vsound : negative!!! sound f sound v v source source f The frequency becomes lower: lower tone 25

26 doppler effect: you moving towards the source v sound additional per second : wavefronts detected source you v observer f f v observer f v observer v v sound sound 26

27 doppler effect: you moving away from the source v sound source you additional wavefronts detected per second : v observer v observer f f f v : negative observer v observer v v sound sound 27

28 doppler effect: general source you f f v v v v observer source v observer : positive if moving towards to source v source : positive if moving towards the observer 28

29 question An ambulance is moving towards you with its sirens on. The frequency of the sound you hear is than the frequency you would hear if the ambulance were not moving at all. a) higher b) the same c) lower f f v v v v observer source 29

30 applications of doppler effect: weather radar Both humidity (reflected intensity) and speed of clouds (doppler effect) are measured. 30

31 example A police car using its siren (frequency 1200Hz) is driving west towards you over Grand River with a velocity of 25m/s. You are driving east over grand river, also with 25m/s. a)what is the frequency of the sound from the siren that you hear? b) What would happen if you were also driving west (behind the ambulance)? v sound =343 m/s a) b) 31

32 applications of the doppler effect: speed radar f f v v v v observer source f v v v approachingcar 32

33 Interference Two traveling waves pass through each other without affecting each other. The resulting displacement is the superposition of the two individual waves. example: two pulses on a string that meet 33

34 v 1 v 2 superposition Interference Constructive interference: maxima line up. Waves are in phase time t 1 Destructive interference: maxima lines up with minimum. Waves are out of phase by ½ time t 2 34

35 Standing wave v 1 v 2 if two waves travel in opposite directions and v 1 =v 2, the superposition of the two waves produces a standing wave: maxima and minima always appear at the same location 35

36 standing waves in a guitar string waves in the string travel back and forth and create standing waves. a wave bouncing back from a fixed point, returns inverted 36

37 we can produce different wave lengths L L L 1 =2L 2 =L 3 =2L/3 L L 4 =2L/4 5 =2L/5 both ends fixed n =2L/n or L=n n /2 37

38 standing waves both ends fixed n =2L/n or L=n n /2 f n f n f f v 1 2 n nv 2L v 2L 2v 2L nv 2L nf 1 n 2L F f 1 : fundamental frequency nth harmonics F: tension in rope : mass per unit length 38

39 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 f n 2L F tension can be varied by stretching the wire changes from string to string: bass string is very heavy length can be chosen by placing fingers 39

40 beats Superposition of 2 waves with slightly different frequency The amplitude changes as a function of time, so the intensity of sound changes as a function of time. The beat frequency (number of intensity maxima/minima per second): f beat = f a -f b 40

41 example A guitar string is struck. Assume that the first harmonic is only excited. What happens to the frequency if: a) The player put a finger at half the length of 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? 41

42 example Someone is trying to tune a guitar. One of the strings is supposed to have a frequency of 500 Hz. The person is using a tuning fork which produces a sound of exactly this frequency, but while sounding the fork and the playing the guitar, hears a beat in the sound with a frequency of 3 Hz (3 beat per second). a) What is the real frequency of the guitar string? b) By what fraction does the person need to change the tension of the guitar string to tune it properly? 42