Sound Intensity. Sound Level

Transcription

1 Lecture 1 Sound Hearing Sound Intensity Sound Level Assistant Prof. Matthias Möbius mobiusm@tcd.ie

2 Sound Waves Gas, liquid or solid is mechanically disturbed Sound waves are produced Speed of sound in a substance depends on physical properties e.g. (density, temperature) When sound encounters a boundary between substances, some sound energy is transmitted and some reflected Reflection makes ultrasound imaging possible

3 Density of Air Sound Sound Waves (Longitudinal waves) A plucked string will vibrate at its natural frequency and alternately compresses and rarefies the air alongside it. direction rarefaction compression Compressed air >>> increased pressure Rarefied air >>> reduced pressure organised vibrations of air molecules>> sound

4 Sound Sound waves-(variation in air pressure) can cause objects to oscillate Example: ear drum is forced to vibrate in response to the air pressure variation Depending on: intensity of the sound frequency of vibration movement of the ear drum will stimulate nerve cells and the sound will be perceived.

5 Sound Waves Speed of sound (v) in materials Depends on Phase of the material Characteristics of the material (elasticity, density & temperature) In general v v v solids liquids gases Greater in solids because molecules interact more strongly with each other Greater in rigid materials Material Speed (ms -1 ) Air 344 Helium 965 Water 1450 Blood 1570 Body Tissue 1570 Copper 3750 Iron 5000 Glass 5000 Helium has a lower density than air. Resonant frequencies of vocal cavity increase. Spectral distribution of sounds shift to higher frequencies -timbre of sound changes

6 Sound Waves Speed of sound (v) Depends on elasticity and density Solid bar v E E Young s Modulus density Liquid v B B bulk modulus v Gas kt m C p specific heat constant pressure C v specific heat constant volume m molecular mass k Boltzmann s constant T temperature (Kelvin) c c p v

7 Calculate the speed of sound in air at 20 o C =1.4. Boltzmann s constant =1.38x10-23 J/K Avg. mass of air molecule = 47.97x10-27 kg V kt m ( J / K)[( ) K] kg V 343.6ms 1

8 Sound Speed of sound The speed of sound in water is 4.2 times the speed of sound in air. A whistle on land produces a sound wave with frequency f 0. When this sound wave enters water, its frequency is: a) 4.2f 0 b) f 0 c) f 0 /4.2 d) Not enough information given Frequency (f) of a wave is independent of the medium through which the wave travels. It is determined by the frequency of the oscillator that is the source of the waves.

9 Sound Diffraction Longer the wavelength compared to size of opening or object the greater the diffraction Light waves: Wavelengths «dimensions of everyday objects Little diffraction occurs Relatively sharp shadows occur Sound waves: Wavelength size of everyday objects 1 diffraction occurs v 344ms Example 8 1 v 310 ms 500nm 14 f 610 Hz 34.4cm f 1KHz Sound source

10 Hearing Hearing Sound wave enters the ear. Forces exerted on eardrum due to air pressure variations cause it to vibrate. three small bones (hammer, anvil, and stirrup) in the middle ear amplify & transmit forces to fluid filled inner ear through the oval window (very small area compared with eardrum) result pressure x 30 Other amplification characteristics?? The motion of the fluid disturbs hair cells within the Cochlea, which transmit nerve impulses to the brain corresponding to the sound heard. Outer ear Middle Inner ear hammer anvil Oval window Cochlea sound Ear canal stirrup ear drum Ear can detect very low intensity sounds

11 Hearing All waves carry energy Audible sound waves carries very little energy Ear can detect extremely low intensity sounds Power output: Talk 10-5 W Talk 24 hours a day non stop for 114 years 10 6 hours Total energy output is 10-5 w x10 6 hrs =10 Wh Equivalent to quantity of energy consumed by a 100W bulb in 6 minutes

12 Sound Waves Intensity Waves (energy) spread out from source Intensity (I) of a wave is defined as Energy (E) carried per unit time per unit area (A) I E/ t A Power (P) P E t therefore I P A Unit of intensity Watt per square metre (Wm -2 ) Sunlight intensity at Earth 10 3 Wm -2

13 Intensity Hearing Human ear can detect extremely low intensities Wm -2 Maximum intensity without ear damage 1 Wm -2 Large range logarithmic units useful Human perception If we listen to two sounds (I 1 and I 2 ) and I 2 seems twice as loud as I 1 Measure intensities I 2 is approximately 6 to 10 times I 1 Convenient scale to measure loudness is the logarithm of the intensity

14 Hearing Perceived loudness is roughly Logarithmic Ear response to sound logarithmic not linear Decibel scale for intensity Sound (Intensity) level in decibels (b) b I0 10 I 10log10 I Wm where (threshold of hearing at 1000Hz) decibel (b) is a relative sound level measurement Threshold of discomfort = 1 Wm -2 Above this, pain is experienced, and there is potential for long term damage

15 Logarithm Logarithm is the inverse of exponentiation: 10 x =120 log 10 (10 x ) = log 10 (120) x log 10 (10) = log 10 (120) x=log 10 (120) Note that logarithms can have different bases. The most common ones are: log 10, log 2, ln (natural logarithm with base e) log(a b) = log(a) + log(b) log(a/b) = log(a) - log(b) log(a b ) = b log(a) log(1) = 0 for all bases Convert between different bases: log x (A) = log y (a) / log y (x)

16 Hearing Sensitivity of ear Can detect sound intensity of Wm -2 Corresponds to pressure variation of 3x10-5 Pa (Atm. Pressure 101,325 Pa) Random fluctuation due to thermal motion of molecules 5x10-6 Pa Sensitivity: essentially due to mechanical layout Area ratio: ear drum to oval window 30 hammer, anvil and stirrup amplification 2 canal resonance at 3kHz pressure increase 2 Total pressure amplification 30x2x2 = 120 Intensity ( pressure ) Intensity increases by factor of =14,400 2 Brain: discriminatory role Filters unwanted noise Suppression: non-awareness of background noise ear is not equally sensitive at all frequencies

17 Sound levels and Intensities Sound level (db) Intensity (Wm -2 ) Sounds 0 1x10-12 Threshold of hearing 10 1x x x10-9 Quiet room 40 1x10-8 computer 50 1x x10-6 Normal conversation 70 1x10-5 Busy traffic 80 1x10-4 Loud radio 90 1x x x Rock concert, Threshold of pain 140 1x10 2 Jet airplane at 30m 160 1x10 4 Bursting eardrums Vibration amplitude. air molecules 1.1x10-11 m 1mm Computer 10 times louder than quiet room Does not seem so because of the logarithmic response of the ear

18 Sound levels and Intensities D a n g e r H e a r i n g l o s s Damage Threshold 5 hours/week at > 89dB damage after 5 years > 100dB deemed hazardous 10 minutes at 120dB Temporarily changes your threshold of hearing from 0dB to 30dB

19 Sound Waves (a) Calculate the sound level in db of a sound intensity 10-8 Wm -2 (b) Calculate the intensity in Wm -2 of a sound level of 80 db I (a) b 10log10 I Wm b 10log Wm b 4 10log d b (b) log I 10 I0 8 log I 10 I0 I I I Wm 10 Wm I 10 Wm 4 2

20 Hearing Hearing ability Loudness is a method of describing the acoustic pressure (or the intensity) of a given sound Intensity hearing range: Wm -2 1Wm -2 Ability to hear is not only a function of intensity but also frequency Humans: Frequency range: 20 Hz 20 khz Infrasonic < 20 Hz Elephants: down to 1Hz Pigeons: down to 0.1 Hz 20 khz < ultrasonic Dogs: up to 40 khz Dolphins: up to 250 khz. Bats: up to 120 khz

21 Hearing Intensity W/m Sound Level db Pain threshold Human Hearing Ability Hearing threshold k 10k 20k Hz frequency Hearing ability as a function of intensity and frequency. The blue solid line is the pure tone threshold curve, below which the subject does not hear. Ear most sensitive at 3000 Hz Pain threshold almost frequency independent

22 Hearing Why two ears Main advantage Sounds from different directions arrive at each of our ears at slightly different times and with slightly different intensities. Time difference of sound arriving at both ears used to locate the source of the sound Example: crossing a road direction of the car approximately how close it is Other advantages easier to understand speech in noisy background help judge loudness

23 Distance Sound intensity is reduced by moving away from source By how much? Inverse Square Law Consider imaginary spheres Isotropic source r 1 Sound intensity r 2 Intensity I P power area P r 2 4 r I I r I r1 As the person gets further away, the sphere that intersects with them gets larger and larger Fraction = Area of person 4 π r 1 2 Fraction = Area of person 4 π r 2 2

24 Sound intensity Variation of Sound Intensity with distance from a point source Inverse square law Intensity I 1 at a distance r 1 from source Intensity I 2 at a distance r 2 from source I I r r1 Intensity is inversely proportional to the square of the distance from the source. NOTE: Sound level (db) is not inversely proportional to distance squared!

25 Sound intensity Examples The intensity falls off as 1/r 2 (where r is the distance) so moving 4 times as far away will decrease the exposure by a factor of 16. A person near a source of loud noise wants to decrease their exposure to it by a factor of 10. How far away do they have to move? I I r r1 I I 10 r r1 10 r r r r They have to move 3.16 times further away

26 Waves Example A bat can detect sound frequencies up to 120,000 Hz. What is the wavelength of sound in the air at this frequency? v f 1 v 344ms f 120, 000Hz 3 v f metres =.287cms High frequency short wavelength Wave only disturbed by objects with dimensions similar to or greater than the wavelength Smaller objects have little effect Bats use ultrasound for navigation Can distinguish between insect and falling leaf

27 Waves Resonance Most objects have a natural frequency: Determined by size shape composition Simple pendulum Only one natural frequency T 1 f 2 l g Resonance occurs if frequency of the driving force equals natural frequency of the system Example: child being pushed on a swing. Swing is kept in motion at its natural frequency by a series of appropriately timed pushes. Difficult to get it to swing at any other frequency If an object is subjected to an intense wave oscillating at object s natural frequency a large response (Resonance) occurs

28 Waves Resonance: examples Opera singers with powerful voices can set glasses into audible vibration If frequency of note is the same as the natural frequency of the glass, the glass may vibrate with a large amplitude and may break Roman foot soldiers were instructed to break step when marching over a bridge Prevented possible resonance response and bridge damage Air passages of the mouth, larynx Nasal cavity together form an acoustic resonator. Voiced sound depend on resonant frequencies of the total system depends on system s volume and shape

29 Resonance: examples Half-closed pipe Resonance (e.g. ear canal): f Resonance / Fundamental mode: Electrical Resonance: Example: Tuning in radio station Adjust resonant frequency of the electrical circuit to the broadcast frequency of the radio station To pick up signal sound f1 sound /(4L)

30 Sound Waves Travel distance is a function of frequency Traveling waves transfer energy from one place to another Sound energy dissipates to thermal energy when sound travels in air. Higher frequency sounds dissipate more quickly, because more energy transferred to the medium; so lower frequency sounds travel further. Examples foghorns have a low frequency Elephants communicate over long distances (up to 4 km), frequencies as low as 14 Hz

31 Lecture 2 Sound Beats Doppler Effect Ultrasound Applications

32 Waves Superposition Simple case: Addition of two waves with same frequency and amplitude Wave 1 Wave 2 resultant Beats If the two waves interfering have slightly different frequencies (wavelengths), beats occur. In step (in phase) In step (in phase) Out of step (out of phase)

33 Waves Beats If the two waves interfering have slightly different frequencies (wavelengths), beats occur. Wave 1 Wave 2 Resultant envelope Waves get in and out of step as time progresses Result- constructive and destructive interference occurs alternately Amplitude changes periodically at the beat frequency Beat frequency f b = f 1 -f 2 Absolute value: beat frequency always positive

34 Waves Beats f b = f 1 -f 2 If frequency difference = zero No beats occur Wave 1 Wave 2 resultant

35 Waves Beats Beats can happen with any type of waves Sound waves Beats perceived as a modulated sound: loudness varies periodically at the beat frequency Application Accurate determination of frequency Example Piano tuning Adjust tension in wire and listen for beats between it and a tuning fork of known frequency The two frequencies are equal when the beats cease. Easier to determine than when listening to individual sounds of nearly equal frequencies f 1 = 264Hz f 2 = 266 Hz Beat frequency 2Hz

36 Sound Waves Doppler Effect Change in perceived frequency depending on the relative motion of the source and listener. Occurs with all types of waves most notable sound waves, light waves. Christian Doppler Austrian Physicist, Mathematician Example: Perceived pitch (or frequency) of a moving source such as a fire engine siren changes as it goes past Frequency of sound emitted does not change Longer Lower f stationary Shorter higher f moving

37 Waves Doppler effect is observed because the distance between the source of sound and the observer is changing. source always emits the same frequency. Source moving towards the observer sound waves reaching observer perceived to be at a more frequent rate (higher frequency) sound waves compressed into shorter distance Source moving away from the observer, sound waves reaching observer perceived to be at a less frequent rate (lower frequency) Sound waves expanded into longer distance

38 Waves Observed frequency for a moving source f observer v wave v wave + sign: source moving away from observer - sign: source moving towards observer v source f source f Stationary source, moving observer observer v wave v v wave observer f source +sign: observer moving towards source - sign: observer moving away from source f = Frequency v = Speed

39 Waves Example moving observer A stationary siren has a frequency of 1000 Hz. What frequency will be heard by drivers of cars moving at 15ms 1? a) away from the siren? b) toward the siren? (a) f o v f w observer v w v ms 15ms fo 1000Hz 956Hz 1 344ms o v f s wave v v wave observer f source (b) f o v w v w v o f s ms 15ms fo 1000Hz 1044Hz 1 344ms

40 Example: Moving Source A Garda car with a 1000 Hz siren is moving at 20 ms -1. What frequency is heard by a stationary listener when the police car is: a) Moving away from b) approaching the listener If you were to replace the Garda car with 2 stationary sirens emitting at the two frequencies as perceived in (a) and (b), what would be the beat frequency between them? (a) f observer v wave v wave v source f source 1 344ms fobserver 1000Hz 945Hz ms 20ms (b) f observer v wave v wave v source f source 1 344ms fobserver 1000Hz 1062Hz ms 20ms

41 Beat frequency f f f beat a b f 945Hz 1062Hz beat fbeat 117Hz

42 Waves Doppler effect can be used to measure speed of the source Radar: RAdio Detecting And Ranging Police radar uses radio waves: measures Doppler shift to determine speed of car compares frequency of reflected wave from car with that emitted from radar Doppler RADAR Weather Rainstorms, tornadoes Wind sheer at airports Swirling air & water droplets RADAR Wave source

43 Sound Waves Reflection of waves (echoes) Caused by solid object Change in nature of medium Sound waves applications SONAR (sound navigation and ranging) - Underwater navigation and observation Measuring the travel time of sound waves in the ocean can help monitor sea temperatures and global changes

44 Ultrasound Frequency greater than range of human hearing Sound with frequencies above 20 khz Normally 1 20MHz Applications Navigation Diagnostics Surgery Therapeutic Cleaning

45 Bats can determine distance, speed and direction of their prey (using reflection time and Doppler effect) Typical prey: moths (dimensions cms) Bats use ultrasonic echolocation methods to detect their presence. Audible Ultrasound why do bats use ultrasound? 1 v 344ms f 1kHz m 34.4 cm Ultrasound 1 v 344ms f 50kHz m 0.7 cm Ultrasound- Shorter wavelength Reflection, not diffraction occurs at moth. Submarines, dolphins and bats use ultrasound for navigation kHz

46 Ultrasound Medical applications Ultrasound Imaging Ultrasound probe passed over region of interest Reflections of ultrasound pulses from patients occur at interfaces between different tissues of different density Good contrast: reflection from boundaries between materials of nearly the same density Reflection time provides depth information Image constructed from echo and position information

47 Ultrasound Medical applications Ultrasound & Doppler effect can be used to measure Blood flow speed in arteries and veins, measure arterial occlusion Echocardiogram, examination of the heart measure blood flow in and out fetal heart beats pulsation of artery walls Stroke: early warning Monitor blood speed in carotid artery in neck Ultrasonic Doppler flow meter Transmitter Receiver Red blood cell

48 Ultrasound Surgery Ultrasonic scalpel (55kHz) Precise cutting and coagulation Tumour removal Tonsillectomies Medical ultrasound without harmful effects intensity kept low ( 10-2 Wm -2 ) to avoid tissue damage Ultrasound scanning during pregnancy

49 Ultrasound Imaging Why use ultrasound---not audible sound Smallest detail observable one wavelength Audible sound wavelength in tissue 1 v 1570ms 0.5m f 3000Hz Ultrasound wavelength in tissue ms 1cm 150kHz In tissue, higher frequencies are attenuated more Compromise between spatial resolution of image and penetration depth 1MHz: penetration depth 6cm 3MHz: superficial conditions (eg. Tennis elbow etc) Frequency is selected based on the depth of the tissue to be treated. Example: deep heat therapy (low frequency)

50 Ultrasound Example Ultrasound speed =1500m/s in tissue. Using an ultrasound frequency of 2MHz, calculate (a) smallest detail visible (b) time for reflected wave to return to probe from a depth of 5cm (a) v f v 1500 m / s 6 f 2 10 Hz l = 0.75mm (b) time for reflected wave to return to probe t s 20.05m 1 v 1500ms sec

51 Ultrasound Other uses in medicine Destructive effects Intense ultrasound produces large density and pressure changes Results Large stresses Heat is produced in most materials microscopic vapour bubbles formed and implode releasing energy (cavitation) Non-invasive removal of kidney stones Dental applications ultrasonic scalar Consists of a ultrasound probe with a small tip. The ultrasound in combination with water flow effective in plaque and tartar removal

52 Ultrasound Component surface cleaning Component placed in fluid in ultrasonic bath Ultrasound creates a periodic compression and expansion in the fluid. Results in Acoustic cavitation Bubbles formed, grow, and implosively collapse localised heating (>1000K) and high pressures (>100 atmospheres) Result: effective surface cleaning Auto-focus cameras computes time taken (and hence distance of subject) for the reflected ultrasonic sound wave to reach the camera lens position and then sets focus accordingly.

53 Sound Supersonic speed Moving source, approaching listener When speed of source approaches the speed of sound, waves ahead of source come close together. f observer v wave v wave v source f source fobserver approaches infinity Nearly infinite number of wave crests reach observer in very short time At supersonic speeds the waves overlap and there are many points of constructive interference, shock wave results Wave front produced when v is known as a shock wave sonic boom source v wave

54 Sound Supersonic speed vs 0 Circles represent wave fronts emitted from sound source Stationary source v = 0 Speed of sound in air =v s v v s subsonic Waves ahead of source come closer together v v s Mach 1 Waves pile up at front v v s supersonic Waves overlap: Shock wave, Sonic boom.

55 Sound Supersonic speed vt s Circles represent wave fronts emitted from sound source sin vt s vt vt In time interval t Sound wave travels a distance v s t Source travels distance vt Tangent lines lie on surface of cone M Ratio v v object speed speed of sound s is called Mach number M v 1 M v sin s since sin 1 No shock unless v v s M 1

56 Bow sin Waves vwwt vt Speed of boat v > Water wave speed V ww

57 Question What is the speed of ultrasound with a wavelength of 0.25 mm and a frequency of 6 MHz? How does this compare with the speed of sound in air? v f v 610 Hz m ms Compare with speed of sound in air ms 1 344ms

58 Question Lightening strikes 10 km away. (a) How long after the strike will you see the light? (b) How long after the strike will you hear the sound? (a) c = 3*10 8 m/s, s = 10 km, t =? s = vt t = s/v t = (10,000 m)/(3*10 8 m/s) = 3.3*10-5 s (b) v = 344 m/s, s = 10 km, t =? s = vt t = s/v = (10,000 m)/(344 m/s) = 29 s If you hear the sound 3 seconds after you see the lightening how far away is the strike? s = vt =(344 m/s)(3 s) = 1002 m

59 Question (a) What is the sound level in decibels of a sound with an intensity of W/m 2? (b) If you had 3 such sounds what would the sound level be? (a) b I 10log10 I Wm b 10log Wm 10 b 10log b 10 log log1010 b b 103dB (b) Wm b 10log Wm b 10log b 10 log log1010 b b 107.8dB Not equal to 3x103 db! Sound levels are logarithms of intensity